diff --git a/app/LStarPerm.hs b/app/LStarPerm.hs
index 6c4433e..ff426bc 100644
--- a/app/LStarPerm.hs
+++ b/app/LStarPerm.hs
@@ -50,12 +50,12 @@ deriving instance Ord (Orbit k) => Monoid (PermEquivariantMap k v)
 deriving instance Ord (Orbit k) => Semigroup (PermEquivariantMap k v)
 
 lookupP :: (Permutable k, Nominal k, Nominal v, _) => k -> PermEquivariantMap k v -> Maybe v
-lookupP x (PEqMap m) = case catMaybes [Map.lookup (act px) m | px <- allPermuted x] of
-  [] -> Nothing
-  (v:_) -> Just v -- take first hit, maybe this is wrong? I guess for v ~ Bool it's fine?
+lookupP x (PEqMap m) = Map.lookup x m
 
+-- For this algorithm, we do more lookups than inserts, so we make the insert
+-- handle the permutations (at the cost of memory).
 insertP :: (Nominal k, Nominal v, _) => k -> v -> PermEquivariantMap k v -> PermEquivariantMap k v
-insertP k v = PEqMap . Map.insert k v . unPEqMap
+insertP k v = PEqMap . flip (Prelude.foldr (\(pk, pv) -> Map.insert pk pv)) [(pk, pv) | pkv <- allPermuted (k, v), let (pk, pv) = act pkv] . unPEqMap
 
 (!~) :: (Permutable k, Nominal k, Nominal v, _) => PermEquivariantMap k v -> k -> v
 (!~) m k = case lookupP k m of
diff --git a/src/Permutable.hs b/src/Permutable.hs
index 2488809..8b7ad65 100644
--- a/src/Permutable.hs
+++ b/src/Permutable.hs
@@ -78,5 +78,12 @@ instance Permutable (Permuted a) where
 instance Permutable Rat where
   act (Permuted (Perm m) p) = Map.findWithDefault p p m
 
+-- TODO: make all this generic
 instance Permutable a => Permutable [a] where
   act (Permuted f ls) = fmap (\x -> act (Permuted f x)) ls
+
+instance (Permutable a, Permutable b) => Permutable (a, b) where
+  act (Permuted f (a, b)) = (act (Permuted f a), act (Permuted f b))
+
+instance Permutable Bool where
+  act (Permuted _ b) = b