diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # composition-prelude
 
+# 2.0.0.0
+
+  * Fix fixity of various operators
+
 # 1.5.3.0
 
   * Add `between` and `~@~`
diff --git a/composition-prelude.cabal b/composition-prelude.cabal
--- a/composition-prelude.cabal
+++ b/composition-prelude.cabal
@@ -1,6 +1,6 @@
 cabal-version: 1.18
 name: composition-prelude
-version: 1.5.3.1
+version: 2.0.0.0
 license: BSD3
 license-file: LICENSE
 copyright: Copyright: (c) 2017-2018 Vanessa McHale
diff --git a/src/Control/Composition.hs b/src/Control/Composition.hs
--- a/src/Control/Composition.hs
+++ b/src/Control/Composition.hs
@@ -10,9 +10,6 @@
     , (-.**)
     , (-.***)
     , (-.****)
-    -- * Monadic composition
-    , (<=<)
-    , (>=>)
     -- * Monadic postcomposition
     , (<=*<)
     , (<=**<)
@@ -41,6 +38,8 @@
     -- * Tuple helpers
     , both
     -- * Reëxports from base
+    , (<=<)
+    , (>=>)
     , (&)
     , (<&>)
     , fix
@@ -67,6 +66,14 @@
 infixl 8 -$
 infixl 8 ~@~
 infixl 8 <~@~<
+infixr 1 <=*<
+infixr 1 >=*>
+infixr 1 <=**<
+infixr 1 >=**>
+infixr 1 <-=*<
+infixr 1 >-=*>
+infixr 1 <-=**<
+infixr 1 >-=**>
 
 axe :: (Traversable t, Applicative f) => t (a -> f ()) -> a -> f ()
 axe = sequenceA_ .* sequenceA