diff --git a/src/Data/Graph/Haggle/Algorithms/DFS.hs b/src/Data/Graph/Haggle/Algorithms/DFS.hs
index 6b9bbbf..e3a033f 100644
--- a/src/Data/Graph/Haggle/Algorithms/DFS.hs
+++ b/src/Data/Graph/Haggle/Algorithms/DFS.hs
@@ -67,22 +67,25 @@ xdfsWith :: (Graph g)
          -> [c]
 xdfsWith g nextVerts f roots
   | isEmpty g || null roots = []
-  | otherwise = runST $ do
-    bs <- newBitSet (maxVertexId g + 1)
-    res <- foldM (go bs) [] roots
-    return $ reverse res
+  | otherwise =
+    if any (not . (`elem` vertices g)) roots
+    then []
+    else runST $ do
+      bs <- newBitSet (maxVertexId g + 1)
+      res <- foldM (go bs) [] roots
+      return $ reverse res
   where
     go bs acc v = do
-      isMarked <- testBit bs (vertexId v)
+      isMarked <- testBitUnsafe bs (vertexId v)
       case isMarked of
         True -> return acc
         False -> do
-          setBit bs (vertexId v)
+          setBitUnsafe bs (vertexId v)
           nxt <- filterM (notVisited bs) (nextVerts v)
           foldM (go bs) (f v : acc) nxt
 
 notVisited :: BitSet s -> Vertex -> ST s Bool
-notVisited bs v = liftM not (testBit bs (vertexId v))
+notVisited bs v = liftM not (testBitUnsafe bs (vertexId v))
 
 -- | Forward parameterized DFS
 dfsWith :: (Graph g)
@@ -130,17 +133,20 @@ xdffWith :: (Graph g)
          -> [Tree c]
 xdffWith g nextVerts f roots
   | isEmpty g || null roots = []
-  | otherwise = runST $ do
-    bs <- newBitSet (maxVertexId g + 1)
-    res <- foldM (go bs) [] roots
-    return $ reverse res
+  | otherwise =
+    if any (not . (`elem` vertices g)) roots
+    then []
+    else runST $ do
+      bs <- newBitSet (maxVertexId g + 1)
+      res <- foldM (go bs) [] roots
+      return $ reverse res
   where
     go bs acc v = do
-      isMarked <- testBit bs (vertexId v)
+      isMarked <- testBitUnsafe bs (vertexId v)
       case isMarked of
         True -> return acc
         False -> do
-          setBit bs (vertexId v)
+          setBitUnsafe bs (vertexId v)
           nxt <- filterM (notVisited bs) (nextVerts v)
           ts <- foldM (go bs) [] nxt
           return $ T.Node (f v) (reverse ts) : acc
diff --git a/src/Data/Graph/Haggle/Internal/BitSet.hs b/src/Data/Graph/Haggle/Internal/BitSet.hs
index 3e9d1ad..2beb2da 100644
--- a/src/Data/Graph/Haggle/Internal/BitSet.hs
+++ b/src/Data/Graph/Haggle/Internal/BitSet.hs
@@ -2,7 +2,9 @@ module Data.Graph.Haggle.Internal.BitSet (
   BitSet,
   newBitSet,
   setBit,
-  testBit
+  testBit,
+  setBitUnsafe,
+  testBitUnsafe
   ) where
 
 import Control.Monad.ST
@@ -11,6 +13,21 @@ import Data.Vector.Unboxed.Mutable ( STVector )
 import qualified Data.Vector.Unboxed.Mutable as V
 import Data.Word ( Word64 )
 
+-- Note that the implementation here assumes thaththe bit numbers are all
+-- unsigned.  A proper implementation would perhaps use 'Natural' instead of
+-- 'Int', but that would require gratuitous fromEnum/toEnum conversions from all
+-- the other API's that just use 'Int', which has about a 33% performance impact
+-- when measured.
+--
+-- The 'setBit' and 'testBit' operations use V.unsafeRead instead of V.read
+-- (where the latter is roughly 25% slower) because this is an internal module
+-- that is generally always used with a positive 'Int' value, and the value is
+-- also checked against 'sz' (which is also probably superfluous).  In other
+-- words, this module prioritizes performance over robustness and should only be
+-- used when the caller can guarantee positive Int values and otherwise good
+-- behavior.
+
+
 data BitSet s = BS (STVector s Word64) {-# UNPACK #-} !Int
 
 bitsPerWord :: Int
@@ -28,22 +45,31 @@ newBitSet n = do
 
 -- | Set a bit in the bitset.  Out of range has no effect.
 setBit :: BitSet s -> Int -> ST s ()
-setBit (BS v sz) bitIx
+setBit b@(BS _ sz) bitIx
   | bitIx >= sz = return ()
-  | otherwise = do
+  | bitIx < 0 = return ()
+  | otherwise = setBitUnsafe b bitIx
+
+-- |  Set a bit in the bitset.  The specified bit must be in range.
+setBitUnsafe :: BitSet s -> Int -> ST s ()
+setBitUnsafe (BS v _) bitIx = do
     let wordIx = bitIx `div` bitsPerWord
         bitPos = bitIx `mod` bitsPerWord
-    oldWord <- V.read v wordIx
+    oldWord <- V.unsafeRead v wordIx
     let newWord = B.setBit oldWord bitPos
     V.write v wordIx newWord
 
 -- | Return True if the bit is set.  Out of range will return False.
 testBit :: BitSet s -> Int -> ST s Bool
-testBit (BS v sz) bitIx
+testBit b@(BS _ sz) bitIx
   | bitIx >= sz = return False
-  | otherwise = do
+  | bitIx < 0 = return False
+  | otherwise = testBitUnsafe b bitIx
+
+-- | Return True if the bit is set.  The specified bit must be in range.
+testBitUnsafe :: BitSet s -> Int -> ST s Bool
+testBitUnsafe (BS v _) bitIx = do
     let wordIx = bitIx `div` bitsPerWord
         bitPos = bitIx `mod` bitsPerWord
-    w <- V.read v wordIx
+    w <- V.unsafeRead v wordIx
     return $ B.testBit w bitPos
-