diff --git a/ouroboros-consensus/src/ouroboros-consensus/Ouroboros/Consensus/Storage/ChainDB/Impl/ChainSel.hs b/ouroboros-consensus/src/ouroboros-consensus/Ouroboros/Consensus/Storage/ChainDB/Impl/ChainSel.hs
index aa31003273..2a9ef55121 100644
--- a/ouroboros-consensus/src/ouroboros-consensus/Ouroboros/Consensus/Storage/ChainDB/Impl/ChainSel.hs
+++ b/ouroboros-consensus/src/ouroboros-consensus/Ouroboros/Consensus/Storage/ChainDB/Impl/ChainSel.hs
@@ -176,7 +176,7 @@ initialChainSelection immutableDB volatileDB lgrDB tracer cfg varInvalid
         suffixesAfterI :: [NonEmpty (HeaderHash blk)]
         suffixesAfterI = Paths.maximalCandidates succsOf limit (AF.anchorToPoint i)
           where
-            limit = ([], k) <$ loE
+            limit = k <$ loE
 
         constructChain ::
              NonEmpty (HeaderHash blk)
@@ -652,7 +652,7 @@ chainSelectionForBlock cdb@CDB{..} blockCache hdr punish = electric $ do
          -- ^ The current chain and ledger
       -> LoE (AnchoredFragment (Header blk))
          -- ^ LoE fragment
-      -> LoE ([Header blk], Word64)
+      -> LoE Word64
          -- ^ How many extra blocks to select after @b@ at most.
       -> m (Point blk)
     addToCurrentChain succsOf curChainAndLedger loeFrag maxExtra = do
@@ -745,7 +745,7 @@ chainSelectionForBlock cdb@CDB{..} blockCache hdr punish = electric $ do
          -- ^ The current chain (anchored at @i@) and ledger
       -> LoE (AnchoredFragment (Header blk))
          -- ^ LoE fragment
-      -> LoE ([Header blk], Word64)
+      -> LoE Word64
          -- ^ How many extra blocks to select after @b@ at most.
       -> ChainDiff (HeaderFields blk)
          -- ^ Header fields for @(x,b]@
@@ -800,10 +800,16 @@ chainSelectionForBlock cdb@CDB{..} blockCache hdr punish = electric $ do
     -- | How many extra blocks to select at most after the tip of @newBlockFrag@
     -- according to the LoE.
     --
-    -- The result is the pair of a list of blocks (coming from the LoE) that are
-    -- the only one that may be selected and a number of additional blocks after
-    -- that, or 'Nothing' if @newBlockFrag@ forks of a strict prefix of the LoE,
-    -- or if it extends the LoE beyond @k@.
+    -- There are two cases to consider:
+    --
+    -- 1. If @newBlockFrag@ and @loeFrag@ are on the same chain, then we cannot
+    --    select more than @loeLimit@ blocks after @loeFrag@.
+    --
+    -- 2. If @newBlockFrag@ and @loeFrag@ are on different chains, then we
+    --   cannot select more than @loeLimit@ blocks after their intersection.
+    --
+    -- In any case, 'Nothing' is returned if @newBlockFrag@ extends beyond
+    -- what LoE allows.
     computeLoEMaxExtra ::
          (HasHeader x, HeaderHash x ~ HeaderHash blk)
       => LoE (AnchoredFragment (Header blk))
@@ -812,32 +818,26 @@ chainSelectionForBlock cdb@CDB{..} blockCache hdr punish = electric $ do
       -> AnchoredFragment x
          -- ^ The fragment with the new block @b@ as its tip, with the same
          -- anchor as @curChain@.
-      -> Maybe (LoE ([Header blk], Word64))
-    computeLoEMaxExtra LoEDisabled _ = Just LoEDisabled
+      -> Maybe (LoE Word64)
     computeLoEMaxExtra (LoEEnabled loeFrag) newBlockFrag =
-      if
-        -- The LoE suffix is empty, which means that the candidate is either
-        -- exactly the LoE fragment or extends it. We can select @k@ blocks from
-        -- the LoE tip.
-        | AF.null loeSuffix
-        , rollback <= k
-        , extra <- k - rollback
-        -> Just $ LoEEnabled ([], extra)
-
-        -- The rollback is 0 and the LoE suffix is not empty. We can select the
-        -- blocks of the LoE (and only those) and then @k@ more.
-        | rollback == 0
-        -> Just $ LoEEnabled (AF.toOldestFirst loeSuffix, k)
-
-        -- The LoE suffix is not empty and the rollback is not 0, which means
-        -- that the candidate forks off the LoE fragment at some point, but not
-        -- at the tip, which is forbidden.
-        | otherwise
-        -> Nothing
+        -- Both fragments are on the same chain
+        if loeSuffixLength == 0 || rollback == 0 then
+          if rollback <= k + loeSuffixLength
+            then Just $ LoEEnabled $ k + loeSuffixLength - rollback
+            else Nothing
+        else
+          -- REVIEW: Since we filter out candidates that fork off the LoE later,
+          -- it does not really matter what we return here and we could just
+          -- return @Nothing@ or merge it in the previous case.
+          if rollback <= k
+            then Just $ LoEEnabled $ k - rollback
+            else Nothing
       where
         d = Diff.diff newBlockFrag loeFrag
         rollback = Diff.getRollback d
-        loeSuffix = Diff.getSuffix d
+        loeSuffixLength = fromIntegral $ AF.length (Diff.getSuffix d)
+    computeLoEMaxExtra LoEDisabled _ =
+        Just LoEDisabled
 
     mkSelectionChangedInfo ::
          AnchoredFragment (Header blk) -- ^ old chain
diff --git a/ouroboros-consensus/src/ouroboros-consensus/Ouroboros/Consensus/Storage/ChainDB/Impl/Paths.hs b/ouroboros-consensus/src/ouroboros-consensus/Ouroboros/Consensus/Storage/ChainDB/Impl/Paths.hs
index de74213c51..51bec3614c 100644
--- a/ouroboros-consensus/src/ouroboros-consensus/Ouroboros/Consensus/Storage/ChainDB/Impl/Paths.hs
+++ b/ouroboros-consensus/src/ouroboros-consensus/Ouroboros/Consensus/Storage/ChainDB/Impl/Paths.hs
@@ -1,6 +1,5 @@
 {-# LANGUAGE BangPatterns             #-}
 {-# LANGUAGE DisambiguateRecordFields #-}
-{-# LANGUAGE FlexibleContexts         #-}
 {-# LANGUAGE LambdaCase               #-}
 {-# LANGUAGE NamedFieldPuns           #-}
 {-# LANGUAGE ScopedTypeVariables      #-}
@@ -69,17 +68,14 @@ type LookupBlockInfo blk = HeaderHash blk -> Maybe (VolatileDB.BlockInfo blk)
 -- beyond the LoE fragment.
 maximalCandidates ::
      forall blk.
-     ( HasHeader blk
-     , HasHeader (Header blk)
-     )
-  => (ChainHash blk -> Set (HeaderHash blk))
+     (ChainHash blk -> Set (HeaderHash blk))
      -- ^ @filterByPredecessor@
-  -> LoE ([Header blk], Word64) -- ^ Max length of any candidate
+  -> LoE Word64 -- ^ Max length of any candidate
   -> Point blk -- ^ @B@
   -> [NonEmpty (HeaderHash blk)]
      -- ^ Each element in the list is a list of hashes from which we can
      -- construct a fragment anchored at the point @B@.
-maximalCandidates succsOf loeLimit b = mapMaybe ((NE.nonEmpty =<<) . applyLoE) $ go (pointHash b)
+maximalCandidates succsOf loeLimit b = mapMaybe (NE.nonEmpty . applyLoE) $ go (pointHash b)
   where
     go :: ChainHash blk -> [[HeaderHash blk]]
     go mbHash = case Set.toList $ succsOf mbHash of
@@ -89,20 +85,10 @@ maximalCandidates succsOf loeLimit b = mapMaybe ((NE.nonEmpty =<<) . applyLoE) $
                , candidate <- go (BlockHash next)
                ]
     applyLoE
-      | LoEEnabled (loeBlocks, limit) <- loeLimit
-      = applyLoEEnabled loeBlocks limit
-      | otherwise
-      = Just
-    applyLoEEnabled :: [Header blk] -> Word64 -> [HeaderHash blk] -> Maybe [HeaderHash blk]
-    applyLoEEnabled _ _ [] = Just []
-    applyLoEEnabled [] 0 _ = Nothing
-    applyLoEEnabled [] limit (hash : hashes) =
-      (hash :) <$> applyLoEEnabled [] (limit - 1) hashes
-    applyLoEEnabled (loeBlock : loeBlocks) limit (hash : hashes)
-      | blockHash loeBlock == hash
-      = (hash :) <$> applyLoEEnabled loeBlocks limit hashes
+      | LoEEnabled limit <- loeLimit
+      = take (fromIntegral limit)
       | otherwise
-      = Nothing
+      = id
 
 -- | Extend the 'ChainDiff' with the successors found by 'maximalCandidates'.
 --
@@ -115,13 +101,10 @@ maximalCandidates succsOf loeLimit b = mapMaybe ((NE.nonEmpty =<<) . applyLoE) $
 -- Only the longest possible extensions are returned, no intermediary prefixes
 -- of extensions.
 extendWithSuccessors ::
-     forall blk.
-     ( HasHeader blk
-     , HasHeader (Header blk)
-     )
+     forall blk. HasHeader blk
   => (ChainHash blk -> Set (HeaderHash blk))
   -> LookupBlockInfo blk
-  -> LoE ([Header blk], Word64) -- ^ Max extra length for any suffix
+  -> LoE Word64 -- ^ Max extra length for any suffix
   -> ChainDiff (HeaderFields blk)
   -> NonEmpty (ChainDiff (HeaderFields blk))
 extendWithSuccessors succsOf lookupBlockInfo loeLimit diff =