diff --git a/.hlint.yaml b/.hlint.yaml
--- a/.hlint.yaml
+++ b/.hlint.yaml
@@ -49,6 +49,16 @@
     name: Collapse lambdas
     within: Data.Profunctor.Unsafe
 
+- ignore:
+    name: Eta reduce
+    within: Data.Profunctor.Mapping
+
+- ignore:
+    name: "Use tuple-section"
+
+- ignore:
+    name: "Avoid lambda using `infix`"
+
 - fixity: "infixr 9 #."
 - fixity: "infixl 8 .#"
 - fixity: "infixr 0 :->"
diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,151 +1,169 @@
 # This Travis job script has been generated by a script via
 #
-#   runghc make_travis_yml_2.hs '-o' '.travis.yml' '--ghc-head' '--irc-channel=irc.freenode.org#haskell-lens' '--no-no-tests-no-bench' '--no-unconstrained' 'cabal.project'
+#   haskell-ci '--output=.travis.yml' '--config=cabal.haskell-ci' 'cabal.project'
 #
-# For more information, see https://github.com/hvr/multi-ghc-travis
+# For more information, see https://github.com/haskell-CI/haskell-ci
 #
+# version: 0.3.20190425
+#
 language: c
-sudo: false
-
+dist: xenial
 git:
-  submodules: false  # whether to recursively clone submodules
-
+  # whether to recursively clone submodules
+  submodules: false
 notifications:
   irc:
     channels:
-      - "irc.freenode.org#haskell-lens"
+      - irc.freenode.org#haskell-lens
     skip_join: true
     template:
-      - "\x0313profunctors\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}"
-
+      - "\"\\x0313profunctors\\x03/\\x0306%{branch}\\x03 \\x0314%{commit}\\x03 %{build_url} %{message}\""
 cache:
   directories:
     - $HOME/.cabal/packages
     - $HOME/.cabal/store
-
 before_cache:
-  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/build-reports.log
+  - rm -fv $CABALHOME/packages/hackage.haskell.org/build-reports.log
   # remove files that are regenerated by 'cabal update'
-  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/00-index.*
-  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/*.json
-  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.cache
-  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.tar
-  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.tar.idx
-
-  - rm -rfv $HOME/.cabal/packages/head.hackage
-
+  - rm -fv $CABALHOME/packages/hackage.haskell.org/00-index.*
+  - rm -fv $CABALHOME/packages/hackage.haskell.org/*.json
+  - rm -fv $CABALHOME/packages/hackage.haskell.org/01-index.cache
+  - rm -fv $CABALHOME/packages/hackage.haskell.org/01-index.tar
+  - rm -fv $CABALHOME/packages/hackage.haskell.org/01-index.tar.idx
+  - rm -rfv $CABALHOME/packages/head.hackage
 matrix:
   include:
-    - compiler: "ghc-8.6.1"
+    - compiler: ghc-8.8.1
+      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.8.1","cabal-install-3.0"]}}
       env: GHCHEAD=true
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-8.6.1], sources: [hvr-ghc]}}
-    - compiler: "ghc-8.4.3"
-    # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-8.4.3], sources: [hvr-ghc]}}
-    - compiler: "ghc-8.2.2"
-    # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-8.2.2], sources: [hvr-ghc]}}
-    - compiler: "ghc-8.0.2"
-    # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-8.0.2], sources: [hvr-ghc]}}
-    - compiler: "ghc-7.10.3"
-    # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.10.3], sources: [hvr-ghc]}}
-    - compiler: "ghc-7.8.4"
-    # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.8.4], sources: [hvr-ghc]}}
-    - compiler: "ghc-head"
+    - compiler: ghc-8.6.5
+      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.6.5","cabal-install-2.4"]}}
+    - compiler: ghc-8.4.4
+      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.4.4","cabal-install-2.4"]}}
+    - compiler: ghc-8.2.2
+      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.2.2","cabal-install-2.4"]}}
+    - compiler: ghc-8.0.2
+      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.0.2","cabal-install-2.4"]}}
+    - compiler: ghc-7.10.3
+      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.10.3","cabal-install-2.4"]}}
+    - compiler: ghc-7.8.4
+      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.8.4","cabal-install-2.4"]}}
+    - compiler: ghc-head
+      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-head","cabal-install-head"]}}
       env: GHCHEAD=true
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-head], sources: [hvr-ghc]}}
-
   allow_failures:
-    - compiler: "ghc-head"
-    - compiler: "ghc-8.6.1"
-
+    - compiler: ghc-head
+    - compiler: ghc-8.8.1
 before_install:
-  - HC=${CC}
-  - HCPKG=${HC/ghc/ghc-pkg}
+  - HC=$(echo "/opt/$CC/bin/ghc" | sed 's/-/\//')
+  - HCPKG="$HC-pkg"
   - unset CC
-  - export HLINTVER=2.1.3
-  - mkdir ~/.hlint
-  - curl -L https://github.com/ndmitchell/hlint/releases/download/v$HLINTVER/hlint-$HLINTVER-x86_64-linux.tar.gz | tar -xz --strip-components=1 -C ~/.hlint
-  - ROOTDIR=$(pwd)
-  - mkdir -p $HOME/.local/bin
-  - "PATH=~/.hlint:/opt/ghc/bin:/opt/ghc-ppa-tools/bin:$HOME/local/bin:$PATH"
+  - CABAL=/opt/ghc/bin/cabal
+  - CABALHOME=$HOME/.cabal
+  - export PATH="$CABALHOME/bin:$PATH"
+  - TOP=$(pwd)
   - HCNUMVER=$(( $(${HC} --numeric-version|sed -E 's/([0-9]+)\.([0-9]+)\.([0-9]+).*/\1 * 10000 + \2 * 100 + \3/') ))
   - echo $HCNUMVER
-
+  - CABAL="$CABAL -vnormal+nowrap+markoutput"
+  - set -o pipefail
+  - |
+    echo 'function blue(s) { printf "\033[0;34m" s "\033[0m " }'           >> .colorful.awk
+    echo 'BEGIN { state = "output"; }'                                     >> .colorful.awk
+    echo '/^-----BEGIN CABAL OUTPUT-----$/ { state = "cabal" }'            >> .colorful.awk
+    echo '/^-----END CABAL OUTPUT-----$/ { state = "output" }'             >> .colorful.awk
+    echo '!/^(-----BEGIN CABAL OUTPUT-----|-----END CABAL OUTPUT-----)/ {' >> .colorful.awk
+    echo '  if (state == "cabal") {'                                       >> .colorful.awk
+    echo '    print blue($0)'                                              >> .colorful.awk
+    echo '  } else {'                                                      >> .colorful.awk
+    echo '    print $0'                                                    >> .colorful.awk
+    echo '  }'                                                             >> .colorful.awk
+    echo '}'                                                               >> .colorful.awk
+  - cat .colorful.awk
+  - |
+    color_cabal_output () {
+      awk -f $TOP/.colorful.awk
+    }
+  - echo text | color_cabal_output
 install:
-  - cabal --version
+  - ${CABAL} --version
   - echo "$(${HC} --version) [$(${HC} --print-project-git-commit-id 2> /dev/null || echo '?')]"
-  - BENCH=${BENCH---enable-benchmarks}
-  - TEST=${TEST---enable-tests}
-  - HADDOCK=${HADDOCK-true}
-  - UNCONSTRAINED=${UNCONSTRAINED-true}
-  - NOINSTALLEDCONSTRAINTS=${NOINSTALLEDCONSTRAINTS-false}
+  - TEST=--enable-tests
+  - BENCH=--enable-benchmarks
   - GHCHEAD=${GHCHEAD-false}
-  - travis_retry cabal update -v
-  - "sed -i.bak 's/^jobs:/-- jobs:/' ${HOME}/.cabal/config"
-  - rm -fv cabal.project cabal.project.local
-  # Overlay Hackage Package Index for GHC HEAD: https://github.com/hvr/head.hackage
+  - rm -f $CABALHOME/config
   - |
+    echo "verbose: normal +nowrap +markoutput"          >> $CABALHOME/config
+    echo "remote-build-reporting: anonymous"            >> $CABALHOME/config
+    echo "remote-repo-cache: $CABALHOME/packages"       >> $CABALHOME/config
+    echo "logs-dir:          $CABALHOME/logs"           >> $CABALHOME/config
+    echo "world-file:        $CABALHOME/world"          >> $CABALHOME/config
+    echo "extra-prog-path:   $CABALHOME/bin"            >> $CABALHOME/config
+    echo "symlink-bindir:    $CABALHOME/bin"            >> $CABALHOME/config
+    echo "installdir:        $CABALHOME/bin"            >> $CABALHOME/config
+    echo "build-summary:     $CABALHOME/logs/build.log" >> $CABALHOME/config
+    echo "store-dir:         $CABALHOME/store"          >> $CABALHOME/config
+    echo "install-dirs user"                            >> $CABALHOME/config
+    echo "  prefix: $CABALHOME"                         >> $CABALHOME/config
+    echo "repository hackage.haskell.org"               >> $CABALHOME/config
+    echo "  url: http://hackage.haskell.org/"           >> $CABALHOME/config
+  - |
     if $GHCHEAD; then
-      sed -i 's/-- allow-newer: .*/allow-newer: *:base/' ${HOME}/.cabal/config
-      for pkg in $($HCPKG list --simple-output); do pkg=$(echo $pkg | sed 's/-[^-]*$//'); sed -i "s/allow-newer: /allow-newer: *:$pkg, /" ${HOME}/.cabal/config; done
-
-      echo 'repository head.hackage'                                                        >> ${HOME}/.cabal/config
-      echo '   url: http://head.hackage.haskell.org/'                                       >> ${HOME}/.cabal/config
-      echo '   secure: True'                                                                >> ${HOME}/.cabal/config
-      echo '   root-keys: 07c59cb65787dedfaef5bd5f987ceb5f7e5ebf88b904bbd4c5cbdeb2ff71b740' >> ${HOME}/.cabal/config
-      echo '              2e8555dde16ebd8df076f1a8ef13b8f14c66bad8eafefd7d9e37d0ed711821fb' >> ${HOME}/.cabal/config
-      echo '              8f79fd2389ab2967354407ec852cbe73f2e8635793ac446d09461ffb99527f6e' >> ${HOME}/.cabal/config
-      echo '   key-threshold: 3'                                                            >> ${HOME}/.cabal.config
-
-      grep -Ev -- '^\s*--' ${HOME}/.cabal/config | grep -Ev '^\s*$'
-
-      cabal new-update head.hackage -v
+    echo "allow-newer: $($HCPKG list --simple-output | sed -E 's/([a-zA-Z-]+)-[0-9.]+/*:\1/g')" >> $CABALHOME/config
+    
+    echo "repository head.hackage"                                                        >> $CABALHOME/config
+    echo "   url: http://head.hackage.haskell.org/"                                       >> $CABALHOME/config
+    echo "   secure: True"                                                                >> $CABALHOME/config
+    echo "   root-keys: 07c59cb65787dedfaef5bd5f987ceb5f7e5ebf88b904bbd4c5cbdeb2ff71b740" >> $CABALHOME/config
+    echo "              2e8555dde16ebd8df076f1a8ef13b8f14c66bad8eafefd7d9e37d0ed711821fb" >> $CABALHOME/config
+    echo "              8f79fd2389ab2967354407ec852cbe73f2e8635793ac446d09461ffb99527f6e" >> $CABALHOME/config
+    echo "   key-threshold: 3"                                                            >> $CABALHOME/config
     fi
-  - grep -Ev -- '^\s*--' ${HOME}/.cabal/config | grep -Ev '^\s*$'
-  - "printf 'packages: \".\"\\n' > cabal.project"
-  - touch cabal.project.local
-  - "if ! $NOINSTALLEDCONSTRAINTS; then for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/^/constraints: /' | sed 's/-[^-]*$/ installed/' >> cabal.project.local; done; fi"
+  - cat $CABALHOME/config
+  - rm -fv cabal.project cabal.project.local cabal.project.freeze
+  - travis_retry ${CABAL} v2-update -v
+  - if [ $HCNUMVER -eq 80801 ] ; then ${CABAL} v2-install -w ${HC} -j2 hlint --constraint='hlint ==2.1.*' | color_cabal_output ; fi
+  # Generate cabal.project
+  - rm -rf cabal.project cabal.project.local cabal.project.freeze
+  - touch cabal.project
+  - |
+    echo 'packages: "."' >> cabal.project
+  - |
+    echo "write-ghc-environment-files: always" >> cabal.project
+  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | grep -vE -- '^(profunctors)$' | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
   - cat cabal.project || true
   - cat cabal.project.local || true
-  - if [ -f "./configure.ac" ]; then
-      (cd "." && autoreconf -i);
-    fi
-  - rm -f cabal.project.freeze
-  - cabal new-build -w ${HC} ${TEST} ${BENCH} --project-file="cabal.project" --dep -j2 all
-  - rm -rf .ghc.environment.* "."/dist
-  - DISTDIR=$(mktemp -d /tmp/dist-test.XXXX)
-
-# Here starts the actual work to be performed for the package under test;
-# any command which exits with a non-zero exit code causes the build to fail.
+  - if [ -f "./configure.ac" ]; then (cd "." && autoreconf -i); fi
+  - ${CABAL} v2-freeze -w ${HC} ${TEST} ${BENCH} | color_cabal_output
+  - "cat cabal.project.freeze | sed -E 's/^(constraints: *| *)//' | sed 's/any.//'"
+  - rm  cabal.project.freeze
+  - ${CABAL} v2-build -w ${HC} ${TEST} ${BENCH} --dep -j2 all | color_cabal_output
 script:
-  # test that source-distributions can be generated
-  - (cd "." && cabal sdist)
-  - mv "."/dist/profunctors-*.tar.gz ${DISTDIR}/
+  - DISTDIR=$(mktemp -d /tmp/dist-test.XXXX)
+  # Packaging...
+  - ${CABAL} v2-sdist all | color_cabal_output
+  # Unpacking...
+  - mv dist-newstyle/sdist/*.tar.gz ${DISTDIR}/
   - cd ${DISTDIR} || false
   - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
-  - "printf 'packages: profunctors-*/*.cabal\\n' > cabal.project"
-  - touch cabal.project.local
-  - "if ! $NOINSTALLEDCONSTRAINTS; then for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/^/constraints: /' | sed 's/-[^-]*$/ installed/' >> cabal.project.local; done; fi"
+  # Generate cabal.project
+  - rm -rf cabal.project cabal.project.local cabal.project.freeze
+  - touch cabal.project
+  - |
+    echo 'packages: "profunctors-*/*.cabal"' >> cabal.project
+  - |
+    echo "write-ghc-environment-files: always" >> cabal.project
+  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | grep -vE -- '^(profunctors)$' | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
   - cat cabal.project || true
   - cat cabal.project.local || true
-
+  # Building with tests and benchmarks...
   # build & run tests, build benchmarks
-  - cabal new-build -w ${HC} ${TEST} ${BENCH} all
-
-  # cabal check
-  - (cd profunctors-* && cabal check)
-
-  # haddock
-  - rm -rf ./dist-newstyle
-  - if $HADDOCK; then cabal new-haddock -w ${HC} ${TEST} ${BENCH} all; else echo "Skipping haddock generation";fi
-
-  # hlint
-  - hlint --version
-  - (cd profunctors-* && hlint src)
+  - ${CABAL} v2-build -w ${HC} ${TEST} ${BENCH} all | color_cabal_output
+  # HLint..
+  - if [ $HCNUMVER -eq 80801 ] ; then (cd profunctors-* && hlint --cpp-ansi --cpp-define=HLINT src) ; fi
+  # cabal check...
+  - (cd profunctors-* && ${CABAL} -vnormal check)
+  # haddock...
+  - ${CABAL} v2-haddock -w ${HC} ${TEST} ${BENCH} all | color_cabal_output
 
-# REGENDATA ["-o",".travis.yml","--ghc-head","--irc-channel=irc.freenode.org#haskell-lens","--no-no-tests-no-bench","--no-unconstrained","cabal.project"]
+# REGENDATA ["--output=.travis.yml","--config=cabal.haskell-ci","cabal.project"]
 # EOF
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,11 @@
+5.4 [2019.05.10]
+----------------
+* Add `wander`-like combinator `roam` to `Mapping`.
+* Remove illegal `instance Choice (Costar w)`.
+* Add `strong` combinator #62.
+* Only depend on `semigroups` before GHC 8.0.
+* Add `Contravariant` instances for `Star` and `Forget`.
+
 5.3 [2018.07.02]
 ----------------
 * Generalize the types of `(#.)` and `(.#)`. Before, they were:
diff --git a/profunctors.cabal b/profunctors.cabal
--- a/profunctors.cabal
+++ b/profunctors.cabal
@@ -1,6 +1,6 @@
 name:          profunctors
 category:      Control, Categories
-version:       5.3
+version:       5.4
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
@@ -16,8 +16,9 @@
              , GHC == 7.10.3
              , GHC == 8.0.2
              , GHC == 8.2.2
-             , GHC == 8.4.3
-             , GHC == 8.6.1
+             , GHC == 8.4.4
+             , GHC == 8.6.5
+             , GHC == 8.8.1
 build-type:    Simple
 extra-source-files:
   .ghci
@@ -40,9 +41,11 @@
     comonad             >= 4     && < 6,
     contravariant       >= 1     && < 2,
     distributive        >= 0.4.4 && < 1,
-    semigroups          >= 0.11  && < 0.19,
     tagged              >= 0.4.4 && < 1,
     transformers        >= 0.2   && < 0.6
+
+  if !impl(ghc >= 8.0)
+    build-depends: semigroups >= 0.11 && < 0.20
 
   exposed-modules:
     Data.Profunctor
diff --git a/src/Data/Profunctor/Adjunction.hs b/src/Data/Profunctor/Adjunction.hs
--- a/src/Data/Profunctor/Adjunction.hs
+++ b/src/Data/Profunctor/Adjunction.hs
@@ -1,5 +1,4 @@
 {-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE FunctionalDependencies #-}
 {-# LANGUAGE RankNTypes #-}
 -----------------------------------------------------------------------------
diff --git a/src/Data/Profunctor/Choice.hs b/src/Data/Profunctor/Choice.hs
--- a/src/Data/Profunctor/Choice.hs
+++ b/src/Data/Profunctor/Choice.hs
@@ -128,13 +128,6 @@
   right' = right
   {-# INLINE right' #-}
 
--- NB: This instance is highly questionable
-instance Traversable w => Choice (Costar w) where
-  left' (Costar wab) = Costar (either Right Left . fmap wab . traverse (either Right Left))
-  {-# INLINE left' #-}
-  right' (Costar wab) = Costar (fmap wab . sequence)
-  {-# INLINE right' #-}
-
 instance Choice Tagged where
   left' (Tagged b) = Tagged (Left b)
   {-# INLINE left' #-}
diff --git a/src/Data/Profunctor/Closed.hs b/src/Data/Profunctor/Closed.hs
--- a/src/Data/Profunctor/Closed.hs
+++ b/src/Data/Profunctor/Closed.hs
@@ -67,10 +67,10 @@
   closed = (.)
 
 instance Functor f => Closed (Costar f) where
-  closed (Costar fab) = Costar $ \fxa x -> fab (fmap ($x) fxa)
+  closed (Costar fab) = Costar $ \fxa x -> fab (fmap ($ x) fxa)
 
 instance Functor f => Closed (Cokleisli f) where
-  closed (Cokleisli fab) = Cokleisli $ \fxa x -> fab (fmap ($x) fxa)
+  closed (Cokleisli fab) = Cokleisli $ \fxa x -> fab (fmap ($ x) fxa)
 
 instance Distributive f => Closed (Star f) where
   closed (Star afb) = Star $ \xa -> distribute $ \x -> afb (xa x)
diff --git a/src/Data/Profunctor/Mapping.hs b/src/Data/Profunctor/Mapping.hs
--- a/src/Data/Profunctor/Mapping.hs
+++ b/src/Data/Profunctor/Mapping.hs
@@ -1,6 +1,7 @@
 {-# LANGUAGE CPP #-}
 {-# LANGUAGE GADTs #-}
 {-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE DeriveFunctor #-}
 -----------------------------------------------------------------------------
 -- |
 -- Copyright   :  (C) 2015-2018 Edward Kmett
@@ -15,6 +16,8 @@
   ( Mapping(..)
   , CofreeMapping(..)
   , FreeMapping(..)
+  -- * Traversing in terms of Mapping
+  , wanderMapping
   -- * Closed in terms of Mapping
   , traverseMapping
   , closedMapping
@@ -44,17 +47,46 @@
   -- 'dimap' 'Data.Functor.Identity.Identity' 'Data.Functor.Identity.runIdentity' '.' 'map'' ≡ 'id'
   -- @
   map' :: Functor f => p a b -> p (f a) (f b)
+  map' = roam collect
 
+  roam :: (forall f. (Distributive f, Applicative f)
+                   => (a -> f b) -> s -> f t)
+       -> p a b -> p s t
+  roam f = dimap (\s -> Bar $ \afb -> f afb s) lent . map'
+
+newtype Bar t b a = Bar
+  { runBar :: forall f. (Distributive f, Applicative f)
+           => (a -> f b) -> f t }
+  deriving Functor
+
+lent :: Bar t a a -> t
+lent m = runIdentity (runBar m Identity)
+
 instance Mapping (->) where
   map' = fmap
+  roam f g = runIdentity #. f (Identity #. g)
 
 instance (Monad m, Distributive m) => Mapping (Kleisli m) where
   map' (Kleisli f) = Kleisli (collect f)
+#if __GLASGOW_HASKELL__ >= 710
+  roam f = Kleisli #. f .# runKleisli
+#endif
+{-
+For earlier versions, we'd like to use something like
 
+  roam f = (Kleisli . (unwrapMonad .)) #. f .# ((WrapMonad .) . runKleisli)
+
+but it seems WrappedMonad doesn't have a Distributive instance.
+-}
+
 -- see <https://github.com/ekmett/distributive/issues/12>
 instance (Applicative m, Distributive m) => Mapping (Star m) where
   map' (Star f) = Star (collect f)
+  roam f = Star #. f .# runStar
 
+wanderMapping :: Mapping p => (forall f. Applicative f => (a -> f b) -> s -> f t) -> p a b -> p s t
+wanderMapping f = roam f
+
 traverseMapping :: (Mapping p, Functor f) => p a b -> p (f a) (f b)
 traverseMapping = map'
 
@@ -79,10 +111,15 @@
 
 instance Profunctor p => Traversing (CofreeMapping p) where
   traverse' = map'
+  wander f = roam f
 
 instance Profunctor p => Mapping (CofreeMapping p) where
   -- !@(#*&() Compose isn't representational in its second arg or we could use #. and .#
   map' (CofreeMapping p) = CofreeMapping (dimap Compose getCompose p)
+  roam f (CofreeMapping p) =
+     CofreeMapping $
+       dimap (Compose #. fmap (\s -> Bar $ \afb -> f afb s))
+             (fmap lent .# getCompose) p
 
 instance ProfunctorFunctor CofreeMapping where
   promap f (CofreeMapping p) = CofreeMapping (f p)
@@ -113,6 +150,7 @@
 
 instance Traversing (FreeMapping p) where
   traverse' = map'
+  wander f = roam f
 
 instance Mapping (FreeMapping p) where
   map' (FreeMapping l m r) = FreeMapping (fmap l .# getCompose) m (Compose #. fmap r)
diff --git a/src/Data/Profunctor/Rep.hs b/src/Data/Profunctor/Rep.hs
--- a/src/Data/Profunctor/Rep.hs
+++ b/src/Data/Profunctor/Rep.hs
@@ -139,7 +139,7 @@
 
 -- | Default definition for 'closed' given that @p@ is 'Corepresentable'
 closedCorep :: Corepresentable p => p a b -> p (x -> a) (x -> b)
-closedCorep p = cotabulate $ \fs x -> cosieve p (fmap ($x) fs)
+closedCorep p = cotabulate $ \fs x -> cosieve p (fmap ($ x) fs)
 
 instance Corepresentable (->) where
   type Corep (->) = Identity
diff --git a/src/Data/Profunctor/Sieve.hs b/src/Data/Profunctor/Sieve.hs
--- a/src/Data/Profunctor/Sieve.hs
+++ b/src/Data/Profunctor/Sieve.hs
@@ -1,7 +1,6 @@
 {-# LANGUAGE UndecidableInstances #-}
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE FunctionalDependencies #-}
 {-# LANGUAGE Trustworthy #-}
 -----------------------------------------------------------------------------
diff --git a/src/Data/Profunctor/Strong.hs b/src/Data/Profunctor/Strong.hs
--- a/src/Data/Profunctor/Strong.hs
+++ b/src/Data/Profunctor/Strong.hs
@@ -19,6 +19,7 @@
   -- * Strength
     Strong(..)
   , uncurry'
+  , strong
   , Tambara(..)
   , tambara, untambara
   , Pastro(..)
@@ -60,7 +61,7 @@
 -- This describes profunctor strength with respect to the product structure
 -- of Hask.
 --
--- <http://www-kb.is.s.u-tokyo.ac.jp/~asada/papers/arrStrMnd.pdf>
+-- <http://www.riec.tohoku.ac.jp/~asada/papers/arrStrMnd.pdf>
 --
 class Profunctor p => Strong p where
   -- | Laws:
@@ -68,7 +69,7 @@
   -- @
   -- 'first'' ≡ 'dimap' 'swap' 'swap' '.' 'second''
   -- 'lmap' 'fst' ≡ 'rmap' 'fst' '.' 'first''
-  -- 'lmap' ('second' f) '.' 'first'' ≡ 'rmap' ('second' f) '.' 'first'
+  -- 'lmap' ('second'' f) '.' 'first'' ≡ 'rmap' ('second'' f) '.' 'first''
   -- 'first'' '.' 'first'' ≡ 'dimap' assoc unassoc '.' 'first'' where
   --   assoc ((a,b),c) = (a,(b,c))
   --   unassoc (a,(b,c)) = ((a,b),c)
@@ -81,7 +82,7 @@
   -- @
   -- 'second'' ≡ 'dimap' 'swap' 'swap' '.' 'first''
   -- 'lmap' 'snd' ≡ 'rmap' 'snd' '.' 'second''
-  -- 'lmap' ('first' f) '.' 'second'' ≡ 'rmap' ('first' f) '.' 'second''
+  -- 'lmap' ('first'' f) '.' 'second'' ≡ 'rmap' ('first'' f) '.' 'second''
   -- 'second'' '.' 'second'' ≡ 'dimap' unassoc assoc '.' 'second'' where
   --   assoc ((a,b),c) = (a,(b,c))
   --   unassoc (a,(b,c)) = ((a,b),c)
@@ -94,6 +95,9 @@
 uncurry' :: Strong p => p a (b -> c) -> p (a, b) c
 uncurry' = rmap (\(f,x) -> f x) . first'
 {-# INLINE uncurry' #-}
+
+strong :: Strong p => (a -> b -> c) -> p a b -> p a c
+strong f x = dimap (\a -> (a, a)) (\(b, a) -> f a b) (first' x)
 
 instance Strong (->) where
   first' ab ~(a, c) = (ab a, c)
diff --git a/src/Data/Profunctor/Types.hs b/src/Data/Profunctor/Types.hs
--- a/src/Data/Profunctor/Types.hs
+++ b/src/Data/Profunctor/Types.hs
@@ -39,6 +39,7 @@
 import Data.Coerce (Coercible, coerce)
 import Data.Distributive
 import Data.Foldable
+import Data.Functor.Contravariant
 import Data.Monoid hiding (Product)
 import Data.Profunctor.Unsafe
 import Data.Traversable
@@ -98,6 +99,10 @@
   id = Star return
   Star f . Star g = Star $ g >=> f
 
+instance Contravariant f => Contravariant (Star f a) where
+  contramap f (Star g) = Star (contramap f . g)
+  {-# INLINE contramap #-}
+
 ------------------------------------------------------------------------------
 -- Costar
 ------------------------------------------------------------------------------
@@ -214,3 +219,7 @@
 instance Traversable (Forget r a) where
   traverse _ (Forget k) = pure (Forget k)
   {-# INLINE traverse #-}
+
+instance Contravariant (Forget r a) where
+  contramap _ (Forget k) = Forget k
+  {-# INLINE contramap #-}
