diff --git a/src/Data/Equality/Extraction.hs b/src/Data/Equality/Extraction.hs
index 2610cd2..28b368a 100644
--- a/src/Data/Equality/Extraction.hs
+++ b/src/Data/Equality/Extraction.hs
@@ -51,7 +51,7 @@ extractBest :: forall lang cost
             -> CostFunction lang cost -- ^ The cost function to define /best/
             -> ClassId                -- ^ The e-class from which we'll extract the expression
             -> Fix lang               -- ^ The resulting /best/ expression, in its fixed point form.
-extractBest egr cost (flip find egr -> i) = 
+extractBest (rebuild -> egr) cost (flip unsafeFind egr -> i) = 
 
     -- Use `egg`s strategy of find costs for all possible classes and then just
     -- picking up the best from the target e-class.  In practice this shouldn't
@@ -106,7 +106,7 @@ extractBest egr cost (flip find egr -> i) =
     -- with its cost
     nodeTotalCost :: Traversable lang => ClassIdMap (CostWithExpr lang cost) -> ENode lang -> Maybe (CostWithExpr lang cost)
     nodeTotalCost m (Node n) = do
-        expr <- traverse ((`IM.lookup` m) . flip find egr) n
+        expr <- traverse ((`IM.lookup` m) . flip unsafeFind egr) n
         return $ CostWithExpr (cost ((fst . unCWE) <$> expr), (Fix $ (snd . unCWE) <$> expr))
     {-# INLINE nodeTotalCost #-}
 {-# INLINABLE extractBest #-}
diff --git a/src/Data/Equality/Graph.hs b/src/Data/Equality/Graph.hs
index 1e214d0..94ea5e6 100644
--- a/src/Data/Equality/Graph.hs
+++ b/src/Data/Equality/Graph.hs
@@ -25,6 +25,7 @@ module Data.Equality.Graph
 
       -- ** Querying
     , find, canonicalize
+    , unsafeFind, unsafeCanonicalize
 
       -- * Re-exports
     , module Data.Equality.Graph.Classes
@@ -64,10 +65,10 @@ import Data.Equality.Graph.Lens
 -- class it's already represented in will be returned.
 add :: forall l. Language l => ENode l -> EGraph l -> (ClassId, EGraph l)
 add uncanon_e egr =
-    let !new_en = canonicalize uncanon_e egr
+    let !new_en = unsafeCanonicalize uncanon_e egr
 
      in case lookupNM new_en (memo egr) of
-      Just canon_enode_id -> (find canon_enode_id egr, egr)
+      Just canon_enode_id -> (canon_enode_id, egr)
       Nothing ->
 
         let
@@ -140,8 +141,8 @@ merge a b egr0 =
 
   -- Use canonical ids
   let
-      a' = find a egr0
-      b' = find b egr0
+      a' = unsafeFind a egr0
+      b' = unsafeFind b egr0
    in
    if a' == b'
      then (a', egr0)
@@ -219,16 +220,17 @@ rebuild (EGraph uf cls mm wl awl) =
   let
     emptiedEgr = (EGraph uf cls mm mempty mempty)
 
-    wl'   = nubOrd $ bimap (`find` emptiedEgr) (`canonicalize` emptiedEgr) <$> wl
+    wl'   = nubOrd $ bimap (`unsafeFind` emptiedEgr) (`unsafeCanonicalize` emptiedEgr) <$> wl
     egr'  = foldr repair emptiedEgr wl'
 
     awl'  = nubIntOn fst $ first (`find` egr') <$> awl
     egr'' = foldr repairAnal egr' awl'
-  in
-  -- Loop until worklist is completely empty
-  if null (worklist egr'') && null (analysisWorklist egr'')
+   in -- trace ("Normal deduped: " <> show (length wl - length wl') <> ". Anal deduped: " <> show (length awl - length awl')) $!
+
+    -- Loop until worklist is completely empty
+    if null (worklist egr'') && null (analysisWorklist egr'')
      then egr''
-     else rebuild egr'' -- ROMES:TODO: Doesn't seem to be needed at all in the testsuite.
+     else rebuild egr''
 {-# INLINEABLE rebuild #-}
 
 -- ROMES:TODO: find repair_id could be shared between repair and repairAnal?
@@ -272,17 +274,57 @@ repairAnal (repair_id, node) egr =
 -- that their e-class ids are represented by the same e-class canonical ids
 --
 -- canonicalize(𝑓(𝑎,𝑏,𝑐,...)) = 𝑓((find 𝑎), (find 𝑏), (find 𝑐),...)
-canonicalize :: Functor l => ENode l -> EGraph l -> ENode l
-canonicalize (Node enode) eg = Node $ fmap (`find` eg) enode
+--
+-- This operation will force the e-graph to be rebuilt since canonicalizing an
+-- e-node only makes sense on an e-graph in a sound state. See also
+-- 'unsafeCanonicalize'.
+canonicalize :: Language l => ENode l -> EGraph l -> ENode l
+canonicalize n = unsafeCanonicalize n . rebuild
 {-# INLINE canonicalize #-}
 
 -- | Find the canonical representation of an e-class id in the e-graph
+--
+-- This operation will force the e-graph to be rebuilt since finding the
+-- canonical representation of an e-class id only makes sense on an e-graph in
+-- a sound state. See also 'unsafeFind'.
+--
 -- Invariant: The e-class id always exists.
-find :: ClassId -> EGraph l -> ClassId
-find cid = findRepr cid . unionFind
+find :: Language l => ClassId -> EGraph l -> ClassId
+find cid = unsafeFind cid . rebuild
 {-# INLINE find #-}
 
 -- | The empty e-graph. Nothing is represented in it yet.
 emptyEGraph :: Language l => EGraph l
 emptyEGraph = EGraph emptyUF mempty mempty mempty mempty
 {-# INLINE emptyEGraph #-}
+
+-- | Like 'canonicalize' but doesn't force a rebuild.
+--
+-- It's the responsibility of the caller to ensure that the e-graph is in a
+-- sound state, or otherwise know that the result might not represent the
+-- /true/ representative (that one could expect given e.g. congruence), because
+-- until rebuilt, the e-graph invariants aren't maintained.
+--
+-- By using the unsafe variant one might avoid unncessary calls to 'rebuild',
+-- but note that if the e-graph is already built calls to 'rebuild' are
+-- almost instantaneous.
+unsafeCanonicalize :: Functor l => ENode l -> EGraph l -> ENode l
+unsafeCanonicalize (Node enode) eg = Node $ fmap (`unsafeFind` eg) enode
+{-# INLINE unsafeCanonicalize #-}
+
+-- | Like 'find' but doesn't force a rebuild.
+--
+-- It's the responsibility of the caller to ensure that the e-graph is in a
+-- sound state, or otherwise know that the result might not represent the
+-- /true/ representative (that one could expect given e.g. congruence), because
+-- until rebuilt, the e-graph invariants aren't maintained.
+--
+-- By using the unsafe variant one might avoid unncessary calls to 'rebuild',
+-- but note that if the e-graph is already built calls to 'rebuild' are
+-- almost instantaneous.
+--
+-- Invariant: The e-class id always exists.
+unsafeFind :: ClassId -> EGraph l -> ClassId
+unsafeFind cid = findRepr cid . unionFind
+{-# INLINE unsafeFind #-}
+