diff --git a/saw-core/src/Verifier/SAW/SharedTerm.hs b/saw-core/src/Verifier/SAW/SharedTerm.hs
index dc9063e696..41e8f9d39c 100644
--- a/saw-core/src/Verifier/SAW/SharedTerm.hs
+++ b/saw-core/src/Verifier/SAW/SharedTerm.hs
@@ -255,6 +255,7 @@ import Control.Lens
 import Control.Monad.State.Strict as State
 import Control.Monad.Reader
 import Data.Bits
+import Data.List (inits)
 import Data.Maybe
 import qualified Data.Foldable as Fold
 import Data.Foldable (foldl', foldlM, foldrM, maximum)
@@ -286,6 +287,7 @@ import Verifier.SAW.Term.CtxTerm
 import Verifier.SAW.Term.Pretty
 import Verifier.SAW.TypedAST
 import Verifier.SAW.Unique
+import Verifier.SAW.Utils (panic)
 
 #if !MIN_VERSION_base(4,8,0)
 countTrailingZeros :: (FiniteBits b) => b -> Int
@@ -1058,7 +1060,7 @@ instantiateLocalVars sc f initialLevel t0 =
     go' _ tf@(Constant {}) = scTermF sc tf
 
 instantiateVars :: SharedContext
-                -> (DeBruijnIndex -> Either (ExtCns Term) DeBruijnIndex -> IO Term)
+                -> ((Term -> IO Term) -> DeBruijnIndex -> Either (ExtCns Term) DeBruijnIndex -> IO Term)
                 -> DeBruijnIndex -> Term -> IO Term
 instantiateVars sc f initialLevel t0 =
     do cache <- newCache
@@ -1073,14 +1075,14 @@ instantiateVars sc f initialLevel t0 =
 
     go' :: (?cache :: Cache IO (TermIndex, DeBruijnIndex) Term) =>
            DeBruijnIndex -> TermF Term -> IO Term
-    go' l (FTermF (ExtCns ec)) = f l (Left ec)
+    go' l (FTermF (ExtCns ec)) = f (go l) l (Left ec)
     go' l (FTermF tf)       = scFlatTermF sc =<< (traverse (go l) tf)
     go' l (App x y)         = scTermF sc =<< (App <$> go l x <*> go l y)
     go' l (Lambda i tp rhs) = scTermF sc =<< (Lambda i <$> go l tp <*> go (l+1) rhs)
     go' l (Pi i lhs rhs)    = scTermF sc =<< (Pi i <$> go l lhs <*> go (l+1) rhs)
     go' l (LocalVar i)
       | i < l     = scTermF sc (LocalVar i)
-      | otherwise = f l (Right i)
+      | otherwise = f (go l) l (Right i)
     go' _ tf@(Constant {}) = scTermF sc tf
 
 -- | @incVars k j t@ increments free variables at least @k@ by @j@.
@@ -2185,17 +2187,20 @@ getConstantSet t = snd $ go (IntSet.empty, Map.empty) t
         Constant (EC vidx n ty) body -> (idxs, Map.insert vidx (n, ty, body) names)
         _ -> foldl' go acc tf
 
--- | Instantiate some of the external constants
+-- | Instantiate some of the external constants.
+--   Note: this replacement is _not_ applied recursively
+--   to the terms in the replacement map; so external constants
+--   in those terms will not be replaced.
 scInstantiateExt :: SharedContext
                  -> Map VarIndex Term
                  -> Term
                  -> IO Term
 scInstantiateExt sc vmap = instantiateVars sc fn 0
-  where fn l (Left ec) =
+  where fn _rec l (Left ec) =
             case Map.lookup (ecVarIndex ec) vmap of
                Just t  -> incVars sc 0 l t
                Nothing -> scFlatTermF sc $ ExtCns ec
-        fn _ (Right i) = scTermF sc $ LocalVar i
+        fn _ _ (Right i) = scTermF sc $ LocalVar i
 
 {-
 -- RWD: I'm pretty sure the following implementation gets incorrect results when
@@ -2233,12 +2238,12 @@ scExtsToLocals _ [] x = return x
 scExtsToLocals sc exts x = instantiateVars sc fn 0 x
   where
     m = Map.fromList [ (ecVarIndex ec, k) | (ec, k) <- zip (reverse exts) [0 ..] ]
-    fn l e =
+    fn rec l e =
       case e of
         Left ec ->
           case Map.lookup (ecVarIndex ec) m of
-            Just k -> scLocalVar sc (l + k)
-            Nothing -> scFlatTermF sc (ExtCns ec)
+            Just k  -> scLocalVar sc (l + k)
+            Nothing -> scFlatTermF sc . ExtCns =<< traverse rec ec
         Right i ->
           scLocalVar sc (i + length exts)
 
@@ -2247,18 +2252,43 @@ scExtsToLocals sc exts x = instantiateVars sc fn 0 x
 --   occurrences with the appropriate local variables.
 scAbstractExts :: SharedContext -> [ExtCns Term] -> Term -> IO Term
 scAbstractExts _ [] x = return x
-scAbstractExts sc exts x =
-   do let lams = [ (toShortName (ecName ec), ecType ec) | ec <- exts ]
-      scLambdaList sc lams =<< scExtsToLocals sc exts x
+scAbstractExts sc exts x = loop (inits exts) exts
+  where
+    loop :: [[ExtCns Term]] -> [ExtCns Term] -> IO Term
+    loop ([]:bgs) (ec:ecs) =
+      do tm' <- loop bgs ecs
+         scLambda sc (toShortName (ecName ec)) (ecType ec) tm'
+
+    loop (begin:bgs) (ec:ecs) =
+      do tm' <- loop bgs ecs
+         tp' <- scExtsToLocals sc begin (ecType ec)
+         scLambda sc (toShortName (ecName ec)) tp' tm'
+
+    loop _ [] = scExtsToLocals sc exts x
+
+    loop _ _ = panic "scAbstractExts" ["list size mismatch"]
 
 -- | Generalize over the given list of external constants by wrapping
 -- the given term with foralls and replacing the external constant
 -- occurrences with the appropriate local variables.
 scGeneralizeExts :: SharedContext -> [ExtCns Term] -> Term -> IO Term
 scGeneralizeExts _ [] x = return x
-scGeneralizeExts sc exts x =
-  do let pis = [ (toShortName (ecName ec), ecType ec) | ec <- exts ]
-     scPiList sc pis =<< scExtsToLocals sc exts x
+scGeneralizeExts sc exts x = loop (inits exts) exts
+  where
+    loop :: [[ExtCns Term]] -> [ExtCns Term] -> IO Term
+    loop ([]:bgs) (ec:ecs) =
+      do tm' <- loop bgs ecs
+         scPi sc (toShortName (ecName ec)) (ecType ec) tm'
+
+    loop (begin:bgs) (ec:ecs) =
+      do tm' <- loop bgs ecs
+         tp' <- scExtsToLocals sc begin (ecType ec)
+         scPi sc (toShortName (ecName ec)) tp' tm'
+
+    loop _ [] = scExtsToLocals sc exts x
+
+    loop _ _ = panic "scGeneralizeExts" ["list size mismatch"]
+
 
 scUnfoldConstants :: SharedContext -> [VarIndex] -> Term -> IO Term
 scUnfoldConstants sc names t0 = scUnfoldConstantSet sc True (Set.fromList names) t0