diff --git a/what4/src/What4/Expr/App.hs b/what4/src/What4/Expr/App.hs
index f4943f33..19cf6140 100644
--- a/what4/src/What4/Expr/App.hs
+++ b/what4/src/What4/Expr/App.hs
@@ -194,7 +194,7 @@ data App (e :: BaseType -> Type) (tp :: BaseType) where
   -- Invariant: The BoolMap must contain at least two elements. No
   -- element may be a NotPred; negated elements must be represented
   -- with Negative element polarity.
-  ConjPred :: !(BoolMap e) -> App e BaseBoolType
+  ConjPred :: !(BM.ConjMap e) -> App e BaseBoolType
 
   ------------------------------------------------------------------------
   -- Semiring operations
@@ -814,6 +814,9 @@ traverseApp =
     , ( ConType [t|BoolMap|] `TypeApp` AnyType
       , [| BM.traverseVars |]
       )
+    , ( ConType [t|BM.ConjMap|] `TypeApp` AnyType
+      , [| \f cm -> BM.ConjMap <$> BM.traverseVars f (BM.getConjMap cm) |]
+      )
     , ( ConType [t|Ctx.Assignment|] `TypeApp` AnyType `TypeApp` AnyType
       , [| traverseFC |]
       )
@@ -1158,20 +1161,20 @@ asWeightedSum sr x
 asConjunction :: Expr t BaseBoolType -> [(Expr t BaseBoolType, Polarity)]
 asConjunction (BoolExpr True _) = []
 asConjunction (asApp -> Just (ConjPred xs)) =
- case BM.viewBoolMap xs of
-   BoolMapUnit     -> []
-   BoolMapDualUnit -> [(BoolExpr False initializationLoc, Positive)]
-   BoolMapTerms (tm:|tms) -> tm:tms
+ case BM.viewConjMap xs of
+   BM.ConjTrue -> []
+   BM.ConjFalse -> [(BoolExpr False initializationLoc, Positive)]
+   BM.Conjuncts (tm:|tms) -> tm:tms
 asConjunction x = [(x,Positive)]
 
 
 asDisjunction :: Expr t BaseBoolType -> [(Expr t BaseBoolType, Polarity)]
 asDisjunction (BoolExpr False _) = []
 asDisjunction (asApp -> Just (NotPred (asApp -> Just (ConjPred xs)))) =
- case BM.viewBoolMap xs of
-   BoolMapUnit     -> []
-   BoolMapDualUnit -> [(BoolExpr True initializationLoc, Positive)]
-   BoolMapTerms (tm:|tms) -> map (over _2 BM.negatePolarity) (tm:tms)
+ case BM.viewConjMap xs of
+   BM.ConjTrue -> []
+   BM.ConjFalse -> [(BoolExpr True initializationLoc, Positive)]
+   BM.Conjuncts (tm:|tms) -> map (over _2 BM.negatePolarity) (tm:tms)
 asDisjunction x = [(x,Positive)]
 
 asPosAtom :: Expr t BaseBoolType -> (Expr t BaseBoolType, Polarity)
@@ -2086,11 +2089,11 @@ reduceApp sym unary a0 = do
     BaseEq _ x y -> isEq sym x y
 
     NotPred x -> notPred sym x
-    ConjPred bm ->
-      case BM.viewBoolMap bm of
-        BoolMapDualUnit -> return $ falsePred sym
-        BoolMapUnit     -> return $ truePred sym
-        BoolMapTerms tms ->
+    ConjPred cm ->
+      case BM.viewConjMap cm of
+        BM.ConjFalse -> return $ falsePred sym
+        BM.ConjTrue -> return $ truePred sym
+        BM.Conjuncts tms ->
           do let pol (p, Positive) = return p
                  pol (p, Negative) = notPred sym p
              x:|xs <- mapM pol tms
@@ -2337,14 +2340,14 @@ ppApp' a0 = do
 
     NotPred x -> ppSExpr "not" [x]
 
-    ConjPred xs ->
+    ConjPred cm ->
       let pol (x,Positive) = exprPrettyArg x
           pol (x,Negative) = PrettyFunc "not" [ exprPrettyArg x ]
        in
-       case BM.viewBoolMap xs of
-         BoolMapUnit      -> prettyApp "true" []
-         BoolMapDualUnit  -> prettyApp "false" []
-         BoolMapTerms tms -> prettyApp "and" (map pol (toList tms))
+       case BM.viewConjMap cm of
+         BM.ConjTrue -> prettyApp "true" []
+         BM.ConjFalse-> prettyApp "false" []
+         BM.Conjuncts tms -> prettyApp "and" (map pol (toList tms))
 
     RealIsInteger x -> ppSExpr "isInteger" [x]
     BVTestBit i x   -> prettyApp "testBit"  [exprPrettyArg x, showPrettyArg i]
diff --git a/what4/src/What4/Expr/BoolMap.hs b/what4/src/What4/Expr/BoolMap.hs
index 62cb004c..90ada9c0 100644
--- a/what4/src/What4/Expr/BoolMap.hs
+++ b/what4/src/What4/Expr/BoolMap.hs
@@ -11,8 +11,10 @@ laws like commutativity, associativity and resolution.
 -}
 
 {-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE PatternSynonyms #-}
 {-# LANGUAGE PolyKinds #-}
-{-# LANGUAGE ViewPatterns #-}
+
 module What4.Expr.BoolMap
   ( BoolMap
   , var
@@ -30,6 +32,12 @@ module What4.Expr.BoolMap
   , reversePolarities
   , removeVar
   , Wrap(..)
+    -- * 'ConjMap'
+  , ConjMap(..)
+  , ConjMapView(..)
+  , viewConjMap
+  , addConjunct
+  , evalConj
   ) where
 
 import           Control.Lens (_1, over)
@@ -42,6 +50,7 @@ import           Data.Parameterized.Classes
 import           What4.BaseTypes
 import qualified What4.Utils.AnnotatedMap as AM
 import           What4.Utils.IncrHash
+import Data.Coerce (coerce)
 
 -- | Describes the occurrence of a variable or expression, whether it is
 --   negated or not.
@@ -91,6 +100,8 @@ instance OrdF f => Eq (BoolMap f) where
   BoolMap m1 == BoolMap m2 = AM.eqBy (==) m1 m2
   _ == _ = False
 
+instance OrdF f => Semigroup (BoolMap f) where
+  (<>) = combine
 
 -- | Traverse the expressions in a bool map, and rebuild the map.
 traverseVars :: (Applicative m, HashableF g, OrdF g) =>
@@ -182,3 +193,45 @@ reversePolarities (BoolMap m) = BoolMap $! fmap negatePolarity m
 removeVar :: OrdF f => BoolMap f -> f BaseBoolType -> BoolMap f
 removeVar InconsistentMap _ = InconsistentMap
 removeVar (BoolMap m) x = BoolMap (AM.delete (Wrap x) m)
+
+--------------------------------------------------------------------------------
+-- ConjMap
+
+newtype ConjMap f = ConjMap { getConjMap :: BoolMap f }
+  deriving (Eq, Hashable, Semigroup)
+
+-- | Represents the state of a 'ConjMap'. See 'viewConjMap'.
+--
+-- Like 'BoolMapView', but with more specific names for readability.
+data ConjMapView f
+  = ConjFalse
+    -- ^ A 'ConjMap' with no expressions
+  | ConjTrue
+    -- ^ An inconsistent 'ConjMap'
+  | Conjuncts (NonEmpty (f BaseBoolType, Polarity))
+    -- ^ The terms appearing in the 'ConjMap', of which there is at least one
+
+conjMapView :: BoolMapView f -> ConjMapView f
+conjMapView BoolMapUnit = ConjTrue
+conjMapView BoolMapDualUnit = ConjFalse
+conjMapView (BoolMapTerms ts) = Conjuncts ts
+
+-- | Deconstruct the given 'ConjMap' for later processing
+viewConjMap :: ConjMap f -> ConjMapView f
+viewConjMap = conjMapView . viewBoolMap . getConjMap
+{-# INLINE viewConjMap #-}
+
+addConjunct :: (HashableF f, OrdF f) => f BaseBoolType -> Polarity -> ConjMap f -> ConjMap f
+addConjunct t p = coerce (addVar t p)
+{-# INLINE addConjunct #-}
+
+evalConj :: Applicative m => (f BaseBoolType -> m Bool) -> ConjMap f -> m Bool
+evalConj f cm =
+  let pol (x, Positive) = f x
+      pol (x, Negative) = not <$> f x
+  in
+  case viewConjMap cm of
+    ConjTrue -> pure True
+    ConjFalse -> pure False
+    Conjuncts (t:|ts) ->
+      List.foldl' (&&) <$> pol t <*> traverse pol ts
diff --git a/what4/src/What4/Expr/Builder.hs b/what4/src/What4/Expr/Builder.hs
index dc39a467..873d130e 100644
--- a/what4/src/What4/Expr/Builder.hs
+++ b/what4/src/What4/Expr/Builder.hs
@@ -1548,16 +1548,16 @@ realSum sym s = semiRingSum sym s
 bvSum :: ExprBuilder t st fs -> WeightedSum (Expr t) (SR.SemiRingBV flv w) -> IO (BVExpr t w)
 bvSum sym s = semiRingSum sym s
 
-conjPred :: ExprBuilder t st fs -> BoolMap (Expr t) -> IO (BoolExpr t)
-conjPred sym bm =
-  case BM.viewBoolMap bm of
-    BoolMapUnit     -> return $ truePred sym
-    BoolMapDualUnit -> return $ falsePred sym
-    BoolMapTerms ((x,p):|[]) ->
+conjPred :: ExprBuilder t st fs -> BM.ConjMap (Expr t) -> IO (BoolExpr t)
+conjPred sym cm =
+  case BM.viewConjMap cm of
+    BM.ConjTrue -> return $ truePred sym
+    BM.ConjFalse -> return $ falsePred sym
+    BM.Conjuncts ((x,p):|[]) ->
       case p of
         Positive -> return x
         Negative -> notPred sym x
-    _ -> sbMakeExpr sym $ ConjPred bm
+    _ -> sbMakeExpr sym $ ConjPred cm
 
 bvUnary :: (1 <= w) => ExprBuilder t st fs -> UnaryBV (BoolExpr t) w -> IO (BVExpr t w)
 bvUnary sym u
@@ -1985,7 +1985,7 @@ tryAndAbsorption ::
   BoolExpr t ->
   Bool
 tryAndAbsorption (asApp -> Just (NotPred (asApp -> Just (ConjPred as)))) (asConjunction -> bs)
-  = checkAbsorption (BM.reversePolarities as) bs
+  = checkAbsorption (BM.reversePolarities (BM.getConjMap as)) bs
 tryAndAbsorption _ _ = False
 
 
@@ -1997,7 +1997,7 @@ tryOrAbsorption ::
   BoolExpr t ->
   Bool
 tryOrAbsorption (asApp -> Just (ConjPred as)) (asDisjunction -> bs)
-  = checkAbsorption as bs
+  = checkAbsorption (BM.getConjMap as) bs
 tryOrAbsorption _ _ = False
 
 
@@ -2095,7 +2095,7 @@ instance IsExprBuilder (ExprBuilder t st fs) where
    go a b
      | Just (ConjPred as) <- asApp a
      , Just (ConjPred bs) <- asApp b
-     = conjPred sym $ BM.combine as bs
+     = conjPred sym $ as <> bs
 
      | tryAndAbsorption a b
      = return b
@@ -2104,13 +2104,13 @@ instance IsExprBuilder (ExprBuilder t st fs) where
      = return a
 
      | Just (ConjPred as) <- asApp a
-     = conjPred sym $ uncurry BM.addVar (asPosAtom b) as
+     = conjPred sym $ uncurry BM.addConjunct (asPosAtom b) as
 
      | Just (ConjPred bs) <- asApp b
-     = conjPred sym $ uncurry BM.addVar (asPosAtom a) bs
+     = conjPred sym $ uncurry BM.addConjunct (asPosAtom a) bs
 
      | otherwise
-     = conjPred sym $ BM.fromVars [asPosAtom a, asPosAtom b]
+     = conjPred sym $ BM.ConjMap (BM.fromVars [asPosAtom a, asPosAtom b])
 
   orPred sym x y =
     case (asConstantPred x, asConstantPred y) of
@@ -2125,7 +2125,7 @@ instance IsExprBuilder (ExprBuilder t st fs) where
    go a b
      | Just (NotPred (asApp -> Just (ConjPred as))) <- asApp a
      , Just (NotPred (asApp -> Just (ConjPred bs))) <- asApp b
-     = notPred sym =<< conjPred sym (BM.combine as bs)
+     = notPred sym =<< conjPred sym (as <> bs)
 
      | tryOrAbsorption a b
      = return b
@@ -2134,13 +2134,13 @@ instance IsExprBuilder (ExprBuilder t st fs) where
      = return a
 
      | Just (NotPred (asApp -> Just (ConjPred as))) <- asApp a
-     = notPred sym =<< conjPred sym (uncurry BM.addVar (asNegAtom b) as)
+     = notPred sym =<< conjPred sym (uncurry BM.addConjunct (asNegAtom b) as)
 
      | Just (NotPred (asApp -> Just (ConjPred bs))) <- asApp b
-     = notPred sym =<< conjPred sym (uncurry BM.addVar (asNegAtom a) bs)
+     = notPred sym =<< conjPred sym (uncurry BM.addConjunct (asNegAtom a) bs)
 
      | otherwise
-     = notPred sym =<< conjPred sym (BM.fromVars [asNegAtom a, asNegAtom b])
+     = notPred sym =<< conjPred sym (BM.ConjMap (BM.fromVars [asNegAtom a, asNegAtom b]))
 
   itePred sb c x y
       -- ite c c y = c || y
diff --git a/what4/src/What4/Expr/GroundEval.hs b/what4/src/What4/Expr/GroundEval.hs
index 4179cd77..f930719e 100644
--- a/what4/src/What4/Expr/GroundEval.hs
+++ b/what4/src/What4/Expr/GroundEval.hs
@@ -320,15 +320,7 @@ evalGroundApp f a0 = do
       if xv then f y else f z
 
     NotPred x -> not <$> f x
-    ConjPred xs ->
-      let pol (x,Positive) = f x
-          pol (x,Negative) = not <$> f x
-      in
-      case BM.viewBoolMap xs of
-        BM.BoolMapUnit -> return True
-        BM.BoolMapDualUnit -> return False
-        BM.BoolMapTerms (t:|ts) ->
-          foldl' (&&) <$> pol t <*> mapM pol ts
+    ConjPred cm -> BM.evalConj f cm
 
     RealIsInteger x -> (\xv -> denominator xv == 1) <$> f x
     BVTestBit i x ->
diff --git a/what4/src/What4/Expr/VarIdentification.hs b/what4/src/What4/Expr/VarIdentification.hs
index 279ac13e..b42c8870 100644
--- a/what4/src/What4/Expr/VarIdentification.hs
+++ b/what4/src/What4/Expr/VarIdentification.hs
@@ -306,14 +306,14 @@ recurseAssertedAppExprVars scope p e = go e
  go (asApp -> Just (NotPred x)) =
         recordAssertionVars scope (BM.negatePolarity p) x
 
- go (asApp -> Just (ConjPred xs)) =
+ go (asApp -> Just (ConjPred cm)) =
    let pol (x,BM.Positive) = recordAssertionVars scope p x
        pol (x,BM.Negative) = recordAssertionVars scope (BM.negatePolarity p) x
    in
-   case BM.viewBoolMap xs of
-     BM.BoolMapUnit -> return ()
-     BM.BoolMapDualUnit -> return ()
-     BM.BoolMapTerms (t:|ts) -> mapM_ pol (t:ts)
+   case BM.viewConjMap cm of
+     BM.ConjTrue -> return ()
+     BM.ConjFalse -> return ()
+     BM.Conjuncts (t:|ts) -> mapM_ pol (t:ts)
 
  go (asApp -> Just (BaseIte BaseBoolRepr _ c x y)) =
    do recordExprVars scope c
diff --git a/what4/src/What4/Protocol/SMTWriter.hs b/what4/src/What4/Protocol/SMTWriter.hs
index a97e9344..4dfc7213 100644
--- a/what4/src/What4/Protocol/SMTWriter.hs
+++ b/what4/src/What4/Protocol/SMTWriter.hs
@@ -2134,14 +2134,14 @@ appSMTExpr ae = do
       let pol (x,Positive) = mkBaseExpr x
           pol (x,Negative) = notExpr <$> mkBaseExpr x
       in
-      case BM.viewBoolMap xs of
-        BM.BoolMapUnit ->
+      case BM.viewConjMap xs of
+        BM.ConjTrue ->
           return $ SMTExpr BoolTypeMap $ boolExpr True
-        BM.BoolMapDualUnit ->
+        BM.ConjFalse ->
           return $ SMTExpr BoolTypeMap $ boolExpr False
-        BM.BoolMapTerms (t:|[]) ->
+        BM.Conjuncts (t:|[]) ->
           SMTExpr BoolTypeMap <$> pol t
-        BM.BoolMapTerms (t:|ts) ->
+        BM.Conjuncts (t:|ts) ->
           do cnj <- andAll <$> mapM pol (t:ts)
              freshBoundTerm BoolTypeMap cnj
 
diff --git a/what4/src/What4/Protocol/VerilogWriter/Backend.hs b/what4/src/What4/Protocol/VerilogWriter/Backend.hs
index c10b6ed9..da85cc11 100644
--- a/what4/src/What4/Protocol/VerilogWriter/Backend.hs
+++ b/what4/src/What4/Protocol/VerilogWriter/Backend.hs
@@ -156,7 +156,7 @@ appVerilogExpr app =
       e' <- exprToVerilogExpr e
       unop Not e'
     --DisjPred es -> boolMapToExpr False True Or es
-    ConjPred es -> boolMapToExpr True False And es
+    ConjPred es -> boolMapToExpr True False And (BMap.getConjMap es)
 
     -- Semiring operations
     -- We only support bitvector semiring operations
diff --git a/what4/src/What4/Serialize/Printer.hs b/what4/src/What4/Serialize/Printer.hs
index 26fa5707..1d34f5ee 100644
--- a/what4/src/What4/Serialize/Printer.hs
+++ b/what4/src/What4/Serialize/Printer.hs
@@ -479,7 +479,7 @@ convertAppExpr' = go . W4.appExprApp
         go (W4.NotPred e) = do
           s <- goE e
           return $ S.L [ident "notp", s]
-        go (W4.ConjPred bm) = convertBoolMap "andp" True bm
+        go (W4.ConjPred cm) = convertBoolMap "andp" True (BooM.getConjMap cm)
         go (W4.BVSlt e1 e2) = do
           s1 <- goE e1
           s2 <- goE e2