diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,6 +9,12 @@
 
 ## UNRELEASED
 
+* Added some lightweight negative-shrinking based on a simple dependency analysis.
+
+## 3.3.0
+
+* Added suppport for GHC 9.6.2 compiler
+
 ## 3.2.0
 
 * Added support for negative testing via `validFailingAction` and `postconditionOnFailure`
diff --git a/quickcheck-dynamic.cabal b/quickcheck-dynamic.cabal
--- a/quickcheck-dynamic.cabal
+++ b/quickcheck-dynamic.cabal
@@ -1,6 +1,6 @@
 cabal-version:      2.2
 name:               quickcheck-dynamic
-version:            3.2.0
+version:            3.3.0
 license:            Apache-2.0
 license-files:
   LICENSE
@@ -94,7 +94,7 @@
 
   ghc-options:    -rtsopts
   build-depends:
-    , base                 >=4.7 && <5
+    , base
     , containers
     , mtl
     , QuickCheck
diff --git a/src/Test/QuickCheck/StateModel.hs b/src/Test/QuickCheck/StateModel.hs
--- a/src/Test/QuickCheck/StateModel.hs
+++ b/src/Test/QuickCheck/StateModel.hs
@@ -341,7 +341,7 @@
         <> allVariables (underlyingState aState)
         <> go (computeNextState aState act var) steps
 
-instance StateModel state => Arbitrary (Actions state) where
+instance forall state. StateModel state => Arbitrary (Actions state) where
   arbitrary = do
     (as, rejected) <- arbActions initialAnnotatedState 1
     return $ Actions_ rejected (Smart 0 as)
@@ -377,9 +377,21 @@
                       else go (m + 1) n (actionName (polarAction act) : rej)
 
   shrink (Actions_ rs as) =
-    map (Actions_ rs) (shrinkSmart (map (prune . map fst) . shrinkList shrinker . withStates) as)
+    map (Actions_ rs) (shrinkSmart (map (prune . map fst) . concatMap customActionsShrinker . shrinkList shrinker . withStates) as)
     where
+      shrinker :: (Step state, Annotated state) -> [(Step state, Annotated state)]
       shrinker (v := act, s) = [(unsafeCoerceVar v := act', s) | Some act'@ActionWithPolarity{} <- computeShrinkAction s act]
+
+      customActionsShrinker :: [(Step state, Annotated state)] -> [[(Step state, Annotated state)]]
+      customActionsShrinker acts =
+        let usedVars = mconcat [getAllVariables a <> getAllVariables (underlyingState s) | (_ := a, s) <- acts]
+            binding (v := _, _) = Some v `Set.member` usedVars
+            -- Remove at most one non-binding action
+            go [] = [[]]
+            go (p : ps)
+              | binding p = map (p :) (go ps)
+              | otherwise = ps : map (p :) (go ps)
+         in go acts
 
 -- Running state models