diff --git a/intTests/test1945/Makefile b/intTests/test1945/Makefile
new file mode 100644
index 0000000000..ebf9cc47cc
--- /dev/null
+++ b/intTests/test1945/Makefile
@@ -0,0 +1,11 @@
+CC = clang
+CFLAGS = -g -frecord-command-line -O0
+
+all: test.bc
+
+test.bc: test.c
+	$(CC) $(CFLAGS) -c -emit-llvm $< -o $@
+
+.PHONY: clean
+clean:
+	rm -f test.bc
diff --git a/intTests/test1945/test.bc b/intTests/test1945/test.bc
new file mode 100644
index 0000000000..f30cc928b2
Binary files /dev/null and b/intTests/test1945/test.bc differ
diff --git a/intTests/test1945/test.c b/intTests/test1945/test.c
new file mode 100644
index 0000000000..32ff9ad7fa
--- /dev/null
+++ b/intTests/test1945/test.c
@@ -0,0 +1,3 @@
+#include <stdint.h>
+
+void test(uint8_t *x) {}
diff --git a/intTests/test1945/test.saw b/intTests/test1945/test.saw
new file mode 100644
index 0000000000..2475cf87d8
--- /dev/null
+++ b/intTests/test1945/test.saw
@@ -0,0 +1,17 @@
+// Test a use of `llvm_conditional_points_to` where the value that the pointer
+// points to will fail to match against the right-hand side value unless the
+// condition is properly incorporated into the path condition. This serves as
+// a regression test for https://github.com/GaloisInc/saw-script/issues/1945.
+
+let test_spec = do {
+  p <- llvm_alloc (llvm_int 8);
+  x <- llvm_fresh_var "x" (llvm_int 8);
+  llvm_points_to p (llvm_term x);
+
+  llvm_execute_func [p];
+
+  llvm_conditional_points_to {{ x == 1 }} p (llvm_term {{ 1 : [8] }});
+};
+
+m <- llvm_load_module "test.bc";
+llvm_verify m "test" [] false test_spec z3;
diff --git a/intTests/test1945/test.sh b/intTests/test1945/test.sh
new file mode 100755
index 0000000000..2315cc233c
--- /dev/null
+++ b/intTests/test1945/test.sh
@@ -0,0 +1,3 @@
+set -e
+
+$SAW test.saw
diff --git a/src/SAWScript/Crucible/Common/Override.hs b/src/SAWScript/Crucible/Common/Override.hs
index fac57dcb20..8aa06f14de 100644
--- a/src/SAWScript/Crucible/Common/Override.hs
+++ b/src/SAWScript/Crucible/Common/Override.hs
@@ -34,6 +34,10 @@ module SAWScript.Crucible.Common.Override
   , termSub
   , termEqs
   --
+  , OverrideEnv
+  , OverrideEnv'(..)
+  , oeConditionalPred
+  --
   , OverrideFailureReason(..)
   , ppOverrideFailureReason
   , OverrideFailure(..)
@@ -48,6 +52,7 @@ module SAWScript.Crucible.Common.Override
   , addTermEq
   , addAssert
   , addAssume
+  , withConditionalPred
   , readGlobal
   , writeGlobal
   , failure
@@ -75,6 +80,7 @@ module SAWScript.Crucible.Common.Override
 import qualified Control.Exception as X
 import           Control.Lens
 import           Control.Monad (foldM, unless, when)
+import           Control.Monad.Reader (MonadReader(..), ReaderT(..))
 import           Control.Monad.Trans.State hiding (get, put)
 import           Control.Monad.State.Class (MonadState(..))
 import           Control.Monad.Error.Class (MonadError)
@@ -140,8 +146,19 @@ data OverrideState' sym ext = OverrideState
     -- | Substitution for SAW Core external constants
   , _termSub :: Map VarIndex Term
 
-    -- | Equalities of SAW Core terms
-  , _termEqs :: [(Term, ConditionMetadata, Crucible.SimError)]
+    -- | Equalities of SAW Core terms. The four elements of each tuple are:
+    --
+    -- * A 'W4.Pred' representing the path condition for the part of the
+    --   program in which the term equality occurs.
+    --   See @Note [oeConditionalPred]@.
+    --
+    -- * A 'Term' representing the term equality.
+    --
+    -- * A 'ConditionMetadata' value describing the term equality.
+    --
+    -- * A 'Crucible.SimError' to report in the event that the term equality
+    --   fails to hold.
+  , _termEqs :: [(W4.Pred sym, Term, ConditionMetadata, Crucible.SimError)]
 
     -- | Free variables available for unification
   , _osFree :: Set VarIndex
@@ -188,6 +205,76 @@ initialState sym globals allocs terms free loc = OverrideState
   , _osLocation      = loc
   }
 
+--------------------------------------------------------------------------------
+-- ** OverrideEnv
+
+-- | The environment used in the reader portion of `OverrideMatcher'`.
+newtype OverrideEnv' sym = OverrideEnv
+  { _oeConditionalPred :: W4.Pred sym
+    -- ^ The predicate that is used to construct an implication for any
+    --   assumption or assertion as part of the specification.
+    --   See @Note [oeConditionalPred]@.
+  }
+
+-- | `OverrideEnv'` instantiated at type 'Sym'.
+type OverrideEnv = OverrideEnv' Sym
+
+makeLenses ''OverrideEnv'
+
+-- | The initial override matching environment starts with a trivial path
+-- condition of @True@ (i.e., 'W4.truePred). See @Note [oeConditionalPred]@.
+initialEnv ::
+  W4.IsExprBuilder sym =>
+  sym ->
+  OverrideEnv' sym
+initialEnv sym = OverrideEnv
+  { _oeConditionalPred = W4.truePred sym
+  }
+
+{-
+Note [oeConditionalPred]
+~~~~~~~~~~~~~~~~~~~~~~~~
+oeConditionalPred is a predicate that is used to construct an implication for
+any assumption or assertion used in a specification. That is, oeConditionalPred
+can be thought of as the path condition for the part of the specification where
+the assumption/assertion is created. By default, the oeConditionalPred is
+simply `True` (see `initialEnv`), so when an assertion is created, e.g.,
+
+  llvm_assert {{ x == 2*y }};
+
+Then the overall assertion would be `True ==> (x == 2*y)`. An implication with
+`True` as the premise is not very interesting, of course, but other parts of
+the program may add additional premises (see the `withConditionalPred`
+function).
+
+Currently, the only place in SAW where non-trivial `oeConditionalPred`s are
+added is when matching against an `llvm_conditional_points_to` statement. For
+instance, consider this spec (taken from #1945):
+
+  let test_spec = do {
+    p <- llvm_alloc (llvm_int 8);
+    x <- llvm_fresh_var "x" (llvm_int 8);
+    llvm_points_to p (llvm_term x);
+
+    llvm_execute_func [p];
+
+    llvm_conditional_points_to {{ x == 1 }} p (llvm_term {{ 1 : [8] }});
+  };
+
+The `llvm_conditional_points_to` statement in the postcondition generates an
+assertion that checks `x` (the value that `p` points to) against `1 : [8]`. But
+we only want to check this under the assumption that `x` already equals `1` due
+to the `x == 1` part of the `llvm_conditional_points_to` statement. To do this,
+the implementation of `llvm_conditional_points_to` will add `x == 1` to the
+oeConditionalPred. This way, the assertion that gets generated will be:
+
+  (x == 1 /\ True) ==> (x == 1)
+
+Here, leaving out the (x == 1) premise would be catastrophic, as that would
+result in the far more general assertion `True ==> (x == 1)`. (This was
+ultimately the cause of #1945.)
+-}
+
 --------------------------------------------------------------------------------
 -- ** OverrideFailureReason
 
@@ -313,18 +400,19 @@ data RW
 -- the Crucible simulation in order to compute the variable substitution
 -- and side-conditions needed to proceed.
 newtype OverrideMatcher' sym ext rorw m a =
-  OM (StateT (OverrideState' sym ext) (ExceptT (OverrideFailure ext) m) a)
+  OM (ReaderT (OverrideEnv' sym) (StateT (OverrideState' sym ext) (ExceptT (OverrideFailure ext) m)) a)
   deriving (Applicative, Functor, Generic, Generic1, Monad, MonadIO, MonadThrow)
 
 type OverrideMatcher ext rorw a = OverrideMatcher' Sym ext rorw IO a
 
 instance Wrapped (OverrideMatcher' sym ext rorw m a) where
 
+deriving instance Monad m => MonadReader (OverrideEnv' sym) (OverrideMatcher' sym ext rorw m)
 deriving instance Monad m => MonadState (OverrideState' sym ext) (OverrideMatcher' sym ext rorw m)
 deriving instance Monad m => MonadError (OverrideFailure ext) (OverrideMatcher' sym ext rorw m)
 
 instance MonadTrans (OverrideMatcher' sym ext rorw) where
-    lift f = OM $ lift $ lift f
+    lift f = OM $ lift $ lift $ lift f
 
 throwOverrideMatcher :: Monad m => String -> OverrideMatcher' sym ext rorw m a
 throwOverrideMatcher msg = do
@@ -337,7 +425,7 @@ instance Monad m => Fail.MonadFail (OverrideMatcher' sym ext rorw m) where
 -- | "Run" function for OverrideMatcher. The final result and state
 -- are returned. The state will contain the updated globals and substitutions
 runOverrideMatcher ::
-   Monad m =>
+   (Monad m, W4.IsExprBuilder sym) =>
    sym                         {- ^ simulator                       -} ->
    Crucible.SymGlobalState sym {- ^ initial global variables        -} ->
    Map AllocIndex (Pointer' ext sym) {- ^ initial allocation substitution -} ->
@@ -347,31 +435,55 @@ runOverrideMatcher ::
    OverrideMatcher' sym ext md m a {- ^ matching action                 -} ->
    m (Either (OverrideFailure ext) (a, OverrideState' sym ext))
 runOverrideMatcher sym g a t free loc (OM m) =
-  runExceptT (runStateT m (initialState sym g a t free loc))
+  runExceptT (runStateT (runReaderT m (initialEnv sym)) (initialState sym g a t free loc))
 
 addTermEq ::
   Term {- ^ term equality -} ->
   ConditionMetadata ->
   Crucible.SimError {- ^ reason   -} ->
   OverrideMatcher ext rorw ()
-addTermEq t md r =
-  OM (termEqs %= cons (t, md, r))
+addTermEq t md r = do
+  env <- ask
+  let cond = env ^. oeConditionalPred
+  OM (termEqs %= cons (cond, t, md, r))
 
 addAssert ::
-  Monad m =>
+  (MonadIO m, W4.IsExprBuilder sym) =>
   W4.Pred sym       {- ^ property -} ->
   ConditionMetadata ->
   Crucible.SimError {- ^ reason   -} ->
   OverrideMatcher' sym ext rorw m ()
-addAssert p md r =
-  OM (osAsserts %= cons (md,W4.LabeledPred p r))
+addAssert p md r = do
+  sym <- getSymInterface
+  env <- ask
+  p' <- liftIO $ W4.impliesPred sym (env ^. oeConditionalPred) p
+  OM (osAsserts %= cons (md,W4.LabeledPred p' r))
 
 addAssume ::
-  Monad m =>
+  (MonadIO m, W4.IsExprBuilder sym) =>
   W4.Pred sym       {- ^ property -} ->
   ConditionMetadata ->
   OverrideMatcher' sym ext rorw m ()
-addAssume p md = OM (osAssumes %= cons (md,p))
+addAssume p md = do
+  sym <- getSymInterface
+  env <- ask
+  p' <- liftIO $ W4.impliesPred sym (env ^. oeConditionalPred) p
+  OM (osAssumes %= cons (md,p'))
+
+-- | Add an additional premise to the path condition when executing an
+-- `OverrideMatcher'` subcomputation. See @Note [oeConditionalPred]@ for an
+-- explanation of where this is used.
+withConditionalPred ::
+  (MonadIO m, W4.IsExprBuilder sym) =>
+  W4.Pred sym {- ^ The additional premise -} ->
+  OverrideMatcher' sym ext rorw m a {- ^ The subcomputation -} ->
+  OverrideMatcher' sym ext rorw m a
+withConditionalPred premise om = do
+  sym <- getSymInterface
+  env <- ask
+  premise' <- liftIO $ W4.andPred sym premise (env ^. oeConditionalPred)
+  let env' = env & oeConditionalPred .~ premise'
+  local (const env') om
 
 readGlobal ::
   Monad m =>
@@ -397,7 +509,7 @@ failure ::
   W4.ProgramLoc ->
   OverrideFailureReason ext ->
   OverrideMatcher' sym ext md m a
-failure loc e = OM (lift (throwE (OF loc e)))
+failure loc e = OM (lift (lift (throwE (OF loc e))))
 
 getSymInterface :: Monad m => OverrideMatcher' sym ext md m sym
 getSymInterface = OM (use syminterface)
diff --git a/src/SAWScript/Crucible/JVM/Override.hs b/src/SAWScript/Crucible/JVM/Override.hs
index 680686ac8c..1bf1777e67 100644
--- a/src/SAWScript/Crucible/JVM/Override.hs
+++ b/src/SAWScript/Crucible/JVM/Override.hs
@@ -358,9 +358,11 @@ assertTermEqualities ::
   JVMCrucibleContext ->
   OverrideMatcher CJ.JVM md ()
 assertTermEqualities sc cc = do
-  let assertTermEquality (t, md, e) = do
+  let sym = cc ^. jccSym
+  let assertTermEquality (cond, t, md, e) = do
         p <- instantiateExtResolveSAWPred sc cc t
-        addAssert p md e
+        p' <- liftIO $ W4.impliesPred sym cond p
+        addAssert p' md e
   traverse_ assertTermEquality =<< OM (use termEqs)
 
 
diff --git a/src/SAWScript/Crucible/LLVM/Override.hs b/src/SAWScript/Crucible/LLVM/Override.hs
index 44dc4f89e4..8174385b8a 100644
--- a/src/SAWScript/Crucible/LLVM/Override.hs
+++ b/src/SAWScript/Crucible/LLVM/Override.hs
@@ -708,9 +708,11 @@ assertTermEqualities ::
   LLVMCrucibleContext arch ->
   OverrideMatcher (LLVM arch) md ()
 assertTermEqualities sc cc = do
-  let assertTermEquality (t, md, e) = do
+  let sym = cc ^. ccSym
+  let assertTermEquality (cond, t, md, e) = do
         p <- instantiateExtResolveSAWPred sc cc t
-        addAssert p md e
+        p' <- liftIO $ W4.impliesPred sym cond p
+        addAssert p' md e
   traverse_ assertTermEquality =<< OM (use termEqs)
 
 
@@ -1408,14 +1410,28 @@ matchPointsToValue opts sc cc spec prepost md maybe_cond ptr val =
             let badLoadSummary = summarizeBadLoad cc memTy prepost ptr
             case res of
               Crucible.NoErr pred_ res_val -> do
-                pred_' <- case maybe_cond of
-                  Just cond -> do
-                    cond' <- instantiateExtResolveSAWPred sc cc (ttTerm cond)
-                    liftIO $ W4.impliesPred sym cond' pred_
-                  Nothing -> return pred_
+                -- If dealing with an `llvm_conditional_points_to` statement,
+                -- convert the condition to a `Pred`. If dealing with an
+                -- ordinary `llvm_points_to` statement, this condition will
+                -- simply be `True`.
+                cond' <- case maybe_cond of
+                  Just cond ->
+                    instantiateExtResolveSAWPred sc cc (ttTerm cond)
+                  Nothing ->
+                    pure $ W4.truePred sym
+                -- Next, construct an implication involving the condition and
+                -- assert it.
+                pred_' <- liftIO $ W4.impliesPred sym cond' pred_
                 addAssert pred_' md $ Crucible.SimError loc $
                   Crucible.AssertFailureSimError (show $ PP.vcat badLoadSummary) ""
-                pure Nothing <* matchArg opts sc cc spec prepost md res_val memTy val'
+
+                -- Finally, match the value that the pointer points to against
+                -- the right-hand side value in the points_to statement. Make
+                -- sure to execute this match with an extended path condition
+                -- that takes the condition above into account. See also
+                -- Note [oeConditionalPred] in SAWScript.Crucible.Common.Override.
+                withConditionalPred cond' $
+                  pure Nothing <* matchArg opts sc cc spec prepost md res_val memTy val'
               _ -> do
                 pure $ Just $ describeConcreteMemoryLoadFailure mem badLoadSummary ptr
 
diff --git a/src/SAWScript/Crucible/MIR/Override.hs b/src/SAWScript/Crucible/MIR/Override.hs
index 0cee024cc5..666fcec74c 100644
--- a/src/SAWScript/Crucible/MIR/Override.hs
+++ b/src/SAWScript/Crucible/MIR/Override.hs
@@ -96,9 +96,11 @@ assertTermEqualities ::
   MIRCrucibleContext ->
   OverrideMatcher MIR md ()
 assertTermEqualities sc cc = do
-  let assertTermEquality (t, md, e) = do
+  let sym = cc ^. mccSym
+  let assertTermEquality (cond, t, md, e) = do
         p <- instantiateExtResolveSAWPred sc cc t
-        addAssert p md e
+        p' <- liftIO $ W4.impliesPred sym cond p
+        addAssert p' md e
   F.traverse_ assertTermEquality =<< OM (use termEqs)
 
 -- | Assign the given reference value to the given allocation index in