diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,6 +1,6 @@
 # This Travis job script has been generated by a script via
 #
-#   runghc make_travis_yml_2.hs '-o' '.travis.yml' '--irc-channel=irc.freenode.org#haskell-lens' '--no-no-tests-no-bench' '--no-installed' 'cabal.project'
+#   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'
 #
 # For more information, see https://github.com/hvr/multi-ghc-travis
 #
@@ -36,42 +36,45 @@
 
 matrix:
   include:
-    - compiler: "ghc-7.0.4"
+    - compiler: "ghc-8.6.1"
+      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-2.0,ghc-7.0.4], sources: [hvr-ghc]}}
-    - compiler: "ghc-7.2.2"
+      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-2.0,ghc-7.2.2], sources: [hvr-ghc]}}
-    - compiler: "ghc-7.4.2"
+      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-2.0,ghc-7.4.2], sources: [hvr-ghc]}}
-    - compiler: "ghc-7.6.3"
+      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-2.0,ghc-7.6.3], sources: [hvr-ghc]}}
+      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-2.0,ghc-7.8.4], sources: [hvr-ghc]}}
-    - compiler: "ghc-7.10.3"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.8.4], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.6.3"
+      env: HADDOCK=false # Work around https://github.com/haskell/haddock/issues/242
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.6.3], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.4.2"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.0,ghc-7.10.3], sources: [hvr-ghc]}}
-    - compiler: "ghc-8.0.2"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.4.2], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.2.2"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.0,ghc-8.0.2], sources: [hvr-ghc]}}
-    - compiler: "ghc-8.2.2"
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.2.2], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.0.4"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.0,ghc-8.2.2], sources: [hvr-ghc]}}
-    - compiler: "ghc-8.4.1"
-      env: GHCHEAD=true
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-8.4.1], sources: [hvr-ghc]}}
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.0.4], sources: [hvr-ghc]}}
     - compiler: "ghc-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-7.0.4"
     - compiler: "ghc-7.2.2"
-    - compiler: "ghc-8.4.1"
-    - compiler: "ghc-head"
+    - compiler: "ghc-8.6.1"
 
 before_install:
   - HC=${CC}
@@ -88,13 +91,9 @@
   - echo "$(${HC} --version) [$(${HC} --print-project-git-commit-id 2> /dev/null || echo '?')]"
   - BENCH=${BENCH---enable-benchmarks}
   - TEST=${TEST---enable-tests}
-  - | # Work around https://github.com/haskell/haddock/issues/242
-    if [ "${HC}" != "ghc-7.6.3" ]; then
-      HADDOCK=${HADDOCK-true}
-    else
-      HADDOCK=${HADDOCK-false}
-    fi
-  - INSTALLED=${INSTALLED-true}
+  - HADDOCK=${HADDOCK-true}
+  - UNCONSTRAINED=${UNCONSTRAINED-true}
+  - NOINSTALLEDCONSTRAINTS=${NOINSTALLEDCONSTRAINTS-false}
   - GHCHEAD=${GHCHEAD-false}
   - travis_retry cabal update -v
   - "sed -i.bak 's/^jobs:/-- jobs:/' ${HOME}/.cabal/config"
@@ -102,7 +101,8 @@
   # Overlay Hackage Package Index for GHC HEAD: https://github.com/hvr/head.hackage
   - |
     if $GHCHEAD; then
-      sed -i.bak 's/-- allow-newer:.*/allow-newer: *:base, *:template-haskell, *:ghc, *:Cabal/' ${HOME}/.cabal/config
+      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
@@ -112,11 +112,16 @@
       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
     fi
   - grep -Ev -- '^\s*--' ${HOME}/.cabal/config | grep -Ev '^\s*$'
   - "printf 'packages: \".\" \"./examples\"\\n' > cabal.project"
-  - cat 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 cabal.project || true
+  - cat cabal.project.local || true
   - if [ -f "./configure.ac" ]; then
       (cd "." && autoreconf -i);
     fi
@@ -125,7 +130,7 @@
     fi
   - rm -f cabal.project.freeze
   - cabal new-build -w ${HC} ${TEST} ${BENCH} --project-file="cabal.project" --dep -j2 all
-  - rm -rf "."/.ghc.environment.* "./examples"/.ghc.environment.* "."/dist "./examples"/dist
+  - rm -rf .ghc.environment.* "."/dist "./examples"/dist
   - DISTDIR=$(mktemp -d /tmp/dist-test.XXXX)
 
 # Here starts the actual work to be performed for the package under test;
@@ -138,8 +143,10 @@
   - cd ${DISTDIR} || false
   - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
   - "printf 'packages: comonad-*/*.cabal comonad-examples-*/*.cabal\\n' > cabal.project"
-  - cat 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 cabal.project || true
+  - cat cabal.project.local || true
 
   # build & run tests, build benchmarks
   - cabal new-build -w ${HC} ${TEST} ${BENCH} all
@@ -153,5 +160,5 @@
   - rm -rf ./dist-newstyle
   - if $HADDOCK; then cabal new-haddock -w ${HC} ${TEST} ${BENCH} all; else echo "Skipping haddock generation";fi
 
-# REGENDATA ["-o",".travis.yml","--irc-channel=irc.freenode.org#haskell-lens","--no-no-tests-no-bench","--no-installed","cabal.project"]
+# REGENDATA ["-o",".travis.yml","--ghc-head","--irc-channel=irc.freenode.org#haskell-lens","--no-no-tests-no-bench","--no-unconstrained","cabal.project"]
 # EOF
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,9 @@
+5.0.4 [2018.07.01]
+------------------
+* Add `Comonad` instances for `Tagged s` with `s` of any kind. Before the
+  change, `s` had to be of kind `*`.
+* Allow `containers-0.6`.
+
 5.0.3 [2018.02.06]
 ------------------
 * Don't enable `Safe` on GHC 7.2.
diff --git a/comonad.cabal b/comonad.cabal
--- a/comonad.cabal
+++ b/comonad.cabal
@@ -1,6 +1,6 @@
 name:          comonad
 category:      Control, Comonads
-version:       5.0.3
+version:       5.0.4
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
@@ -14,7 +14,7 @@
 synopsis:      Comonads
 description:   Comonads.
 build-type:    Custom
-tested-with:   GHC == 7.0.4, GHC == 7.2.2, GHC == 7.4.2, GHC == 7.6.3, GHC == 7.8.4, GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.1
+tested-with:   GHC == 7.0.4, GHC == 7.2.2, GHC == 7.4.2, GHC == 7.6.3, GHC == 7.8.4, GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.3, GHC == 8.6.1
 extra-source-files:
   .ghci
   .gitignore
@@ -86,7 +86,7 @@
     transformers-compat >= 0.3     && < 1
 
   if flag(containers)
-    build-depends: containers >= 0.3 && < 0.6
+    build-depends: containers >= 0.3 && < 0.7
 
   if flag(contravariant)
     build-depends: contravariant >= 0.2.0.1 && < 2
@@ -132,4 +132,4 @@
     build-depends:
       base,
       comonad,
-      doctest >= 0.11.1 && < 0.14
+      doctest >= 0.11.1 && < 0.17
diff --git a/src/Control/Comonad.hs b/src/Control/Comonad.hs
--- a/src/Control/Comonad.hs
+++ b/src/Control/Comonad.hs
@@ -4,6 +4,9 @@
 #elif __GLASGOW_HASKELL__ >= 702
 {-# LANGUAGE Trustworthy, DefaultSignatures #-}
 #endif
+#if __GLASGOW_HASKELL__ >= 706
+{-# LANGUAGE PolyKinds #-}
+#endif
  -----------------------------------------------------------------------------
 -- |
 -- Module      :  Control.Comonad
@@ -176,6 +179,14 @@
   extract = runIdentity
   {-# INLINE extract #-}
 
+#if __GLASGOW_HASKELL__ >= 706
+-- $
+-- The variable `s` can have any kind.
+-- For example, here it has kind `Bool`:
+-- >>> :set -XDataKinds
+-- >>> extract (Tagged 42 :: Tagged 'True Integer)
+-- 42
+#endif
 instance Comonad (Tagged s) where
   duplicate = Tagged
   {-# INLINE duplicate #-}