diff --git a/CHANGES b/CHANGES
--- a/CHANGES
+++ b/CHANGES
@@ -1,3 +1,9 @@
+* 0.7.0.1: 29 January 2026
+
+  - Add some cautionary comments to `Regular` and `Semi`.  In
+    particular, `Regular` cannot be used to create a lawful semidirect
+    product of a monoid/semigroup with itself. ([#63](https://github.com/diagrams/monoid-extras/issues/63))
+
 * 0.7: 12 May 2025
 
   - Updates to `Data.Monoid.Coproduct`:
diff --git a/monoid-extras.cabal b/monoid-extras.cabal
--- a/monoid-extras.cabal
+++ b/monoid-extras.cabal
@@ -1,5 +1,5 @@
 name:                monoid-extras
-version:             0.7
+version:             0.7.0.1
 synopsis:            Various extra monoid-related definitions and utilities
 description:         Various extra monoid-related definitions and utilities,
                      such as monoid actions, monoid coproducts, semi-direct
diff --git a/src/Data/Monoid/Action.hs b/src/Data/Monoid/Action.hs
--- a/src/Data/Monoid/Action.hs
+++ b/src/Data/Monoid/Action.hs
@@ -39,12 +39,16 @@
 --   * @act (m1 \`mappend\` m2) = act m1 . act m2@
 --
 --   Semigroup instances are required to satisfy the second law but with
---   ('<>') instead of 'mappend'.  Additionally, if the type @s@ has
---   any algebraic structure, @act m@ should be a homomorphism.  For
---   example, if @s@ is also a monoid we should have @act m mempty =
---   mempty@ and @act m (s1 \`mappend\` s2) = (act m s1) \`mappend\`
---   (act m s2)@.
+--   ('<>') instead of 'mappend'.
 --
+--   Additionally, if the type @s@ has any algebraic structure, @act
+--   m@ should typically be a homomorphism.  For example, if @s@ is
+--   also a monoid we should have @act m mempty = mempty@ and @act m
+--   (s1 \`mappend\` s2) = (act m s1) \`mappend\` (act m s2)@.  In
+--   particular, these laws are necessary for the semidirect product
+--   @Semi s m@ to be a valid semigroup/monoid.  For a more
+--   fine-grained treatment of these ideas, see the @lr-acts@ package.
+--
 --   By default, @act = const id@, so for a type @M@ which should have
 --   no action on anything, it suffices to write
 --
@@ -123,7 +127,11 @@
 -- | Any monoid acts on itself by left multiplication.
 --   This newtype witnesses this action:
 --   @'getRegular' $ 'Regular' m1 `'act'` 'Regular' m2 = m1 '<>' m2@
-newtype Regular m = Regular { getRegular :: m }
+--
+--   Note that this typically does NOT satisfy the distributivity law
+--   @m `act` (m1 <> m2) = (m `act` m1) <> (m `act` m2)@, and hence
+--   cannot be used to form a lawful semidirect product of a monoid with itself.
+newtype Regular m = Regular {getRegular :: m}
 
 instance Semigroup m => Action m (Regular m) where
   m1 `act` Regular m2 = Regular $ m1 <> m2
diff --git a/src/Data/Monoid/SemiDirectProduct.hs b/src/Data/Monoid/SemiDirectProduct.hs
--- a/src/Data/Monoid/SemiDirectProduct.hs
+++ b/src/Data/Monoid/SemiDirectProduct.hs
@@ -24,6 +24,18 @@
 --   We think of the @m@ values as a "tag" decorating the @s@ values,
 --   which also affect the way the @s@ values combine.
 --
+--   NOTE: this is only a valid semigroup/monoid if the action of @m@
+--   on @s@ satisfies BOTH:
+--
+--     1. @act@ is a monoid/semigroup homomorphism from @m@ to @(s ->
+--       s)@, that is, @act mempty = id@ and @act (m1 <> m2) = act m1
+--       . act m2@
+--     2. @act m@ is a monoid/semigroup homomorphism for any @m@, that is,
+--       @act m mempty = mempty@ and @act m (s1 <> s2) = act m s1 <> act m s2@.
+--
+--   For a more fine-grained treatment of these ideas, see the
+--   @lr-acts@ package.
+--
 --   We call the monoid @m@ the quotient monoid and the monoid @s@ the
 --   sub-monoid of the semi-direct product. The semi-direct product
 --   @Semi s m@ is an extension of the monoid @s@ with @m@ being the