diff --git a/CHANGELOG.md b/CHANGELOG.md
index e75a6bccde..9500e8b768 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,6 +9,8 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 
 ### Added
 
+  * Obscure loop optimisation (#1110).
+
 ### Removed
 
 ### Changed
diff --git a/src/Futhark/Analysis/SymbolTable.hs b/src/Futhark/Analysis/SymbolTable.hs
index edc200fc10..39a7a1b407 100644
--- a/src/Futhark/Analysis/SymbolTable.hs
+++ b/src/Futhark/Analysis/SymbolTable.hs
@@ -26,6 +26,7 @@ module Futhark.Analysis.SymbolTable
     lookupSubExp,
     lookupAliases,
     lookupLoopVar,
+    lookupLoopParam,
     available,
     consume,
     index,
@@ -40,6 +41,7 @@ module Futhark.Analysis.SymbolTable
     insertFParams,
     insertLParam,
     insertLoopVar,
+    insertLoopMerge,
 
     -- * Misc
     hideCertified,
@@ -154,7 +156,10 @@ data LetBoundEntry lore = LetBoundEntry
 
 data FParamEntry lore = FParamEntry
   { fparamDec :: FParamInfo lore,
-    fparamAliases :: Names
+    fparamAliases :: Names,
+    -- | If a loop parameter, the initial value and the eventual
+    -- result.  The result need not be in scope in the symbol table.
+    fparamMerge :: Maybe (SubExp, SubExp)
   }
 
 data LParamEntry lore = LParamEntry
@@ -235,6 +240,11 @@ lookupLoopVar name vtable = do
   LoopVar e <- entryType <$> M.lookup name (bindings vtable)
   return $ loopVarBound e
 
+lookupLoopParam :: VName -> SymbolTable lore -> Maybe (SubExp, SubExp)
+lookupLoopParam name vtable = do
+  FParam e <- entryType <$> M.lookup name (bindings vtable)
+  fparamMerge e
+
 -- | In symbol table and not consumed.
 available :: VName -> SymbolTable lore -> Bool
 available name = maybe False (not . entryConsumed) . M.lookup name . bindings
@@ -443,7 +453,8 @@ insertFParam fparam = insertEntry name entry
       FParam
         FParamEntry
           { fparamDec = AST.paramDec fparam,
-            fparamAliases = mempty
+            fparamAliases = mempty,
+            fparamMerge = Nothing
           }
 
 insertFParams ::
@@ -464,6 +475,29 @@ insertLParam param = insertEntry name bind
           }
     name = AST.paramName param
 
+-- | Insert entries corresponding to the parameters of a loop (not
+-- distinguishing contect and value part).  Apart from the parameter
+-- itself, we also insert the initial value and the subexpression
+-- providing the final value.  Note that the latter is likely not in
+-- scope in the symbol at this point.  This is OK, and can still be
+-- used to help some loop optimisations detect invariant loop
+-- parameters.
+insertLoopMerge ::
+  ASTLore lore =>
+  [(AST.FParam lore, SubExp, SubExp)] ->
+  SymbolTable lore ->
+  SymbolTable lore
+insertLoopMerge = flip $ foldl' $ flip bind
+  where
+    bind (p, initial, res) =
+      insertEntry (paramName p) $
+        FParam
+          FParamEntry
+            { fparamDec = AST.paramDec p,
+              fparamAliases = mempty,
+              fparamMerge = Just (initial, res)
+            }
+
 insertLoopVar :: ASTLore lore => VName -> IntType -> SubExp -> SymbolTable lore -> SymbolTable lore
 insertLoopVar name it bound = insertEntry name bind
   where
diff --git a/src/Futhark/Optimise/Simplify/Engine.hs b/src/Futhark/Optimise/Simplify/Engine.hs
index cb042a9d33..540464f7f3 100644
--- a/src/Futhark/Optimise/Simplify/Engine.hs
+++ b/src/Futhark/Optimise/Simplify/Engine.hs
@@ -239,6 +239,13 @@ bindArrayLParams ::
 bindArrayLParams params =
   localVtable $ \vtable -> foldl' (flip ST.insertLParam) vtable params
 
+bindMerge ::
+  SimplifiableLore lore =>
+  [(FParam (Wise lore), SubExp, SubExp)] ->
+  SimpleM lore a ->
+  SimpleM lore a
+bindMerge = localVtable . ST.insertLoopMerge
+
 bindLoopVar :: SimplifiableLore lore => VName -> IntType -> SubExp -> SimpleM lore a -> SimpleM lore a
 bindLoopVar var it bound =
   localVtable $ ST.insertLoopVar var it bound
@@ -800,7 +807,7 @@ simplifyExp (DoLoop ctx val form loopbody) = do
   ((loopstms, loopres), hoisted) <-
     enterLoop $
       consumeMerge $
-        bindFParams (ctxparams' ++ valparams') $
+        bindMerge (zipWith withRes (ctx' ++ val') (bodyResult loopbody)) $
           wrapbody $
             blockIf
               ( hasFree boundnames `orIf` isConsumed
@@ -819,6 +826,7 @@ simplifyExp (DoLoop ctx val form loopbody) = do
       localVtable $ flip (foldl' (flip ST.consume)) $ namesToList consumed_by_merge
     consumed_by_merge =
       freeIn $ map snd $ filter (unique . paramDeclType . fst) val
+    withRes (p, x) y = (p, x, y)
 simplifyExp (Op op) = do
   (op', stms) <- simplifyOp op
   return (Op op', stms)
diff --git a/src/Futhark/Optimise/Simplify/Rules.hs b/src/Futhark/Optimise/Simplify/Rules.hs
index e5cc1a367d..abc998b3a1 100644
--- a/src/Futhark/Optimise/Simplify/Rules.hs
+++ b/src/Futhark/Optimise/Simplify/Rules.hs
@@ -153,11 +153,11 @@ removeRedundantMergeVariables _ _ _ _ =
 -- We may change the type of the loop if we hoist out a shape
 -- annotation, in which case we also need to tweak the bound pattern.
 hoistLoopInvariantMergeVariables :: BinderOps lore => TopDownRuleDoLoop lore
-hoistLoopInvariantMergeVariables _ pat aux (ctx, val, form, loopbody) =
+hoistLoopInvariantMergeVariables vtable pat aux (ctx, val, form, loopbody) =
   -- Figure out which of the elements of loopresult are
   -- loop-invariant, and hoist them out.
   case foldr checkInvariance ([], explpat, [], []) $
-    zip merge res of
+    zip3 (patternNames pat) merge res of
     ([], _, _, _) ->
       -- Nothing is invariant.
       Skip
@@ -199,11 +199,11 @@ hoistLoopInvariantMergeVariables _ pat aux (ctx, val, form, loopbody) =
           (Nothing, explpat')
 
     checkInvariance
-      ((mergeParam, mergeInit), resExp)
+      (pat_name, (mergeParam, mergeInit), resExp)
       (invariant, explpat', merge', resExps)
         | not (unique (paramDeclType mergeParam))
             || arrayRank (paramDeclType mergeParam) == 1,
-          isInvariant resExp,
+          isInvariant,
           -- Also do not remove the condition in a while-loop.
           not $ paramName mergeParam `nameIn` freeIn form =
           let (bnd, explpat'') =
@@ -214,21 +214,36 @@ hoistLoopInvariantMergeVariables _ pat aux (ctx, val, form, loopbody) =
                 resExps
               )
         where
-          -- A non-unique merge variable is invariant if the corresponding
-          -- subexp in the result is EITHER:
+          -- A non-unique merge variable is invariant if one of the
+          -- following is true:
           --
-          --  (0) a variable of the same name as the parameter, where
-          --  all existential parameters are already known to be
-          --  invariant
-          isInvariant (Var v2)
-            | paramName mergeParam == v2 =
+          -- (0) The result is a variable of the same name as the
+          -- parameter, where all existential parameters are already
+          -- known to be invariant
+          isInvariant
+            | Var v2 <- resExp,
+              paramName mergeParam == v2 =
               allExistentialInvariant
                 (namesFromList $ map (identName . fst) invariant)
                 mergeParam
-          --  (1) or identical to the initial value of the parameter.
-          isInvariant _ = mergeInit == resExp
-    checkInvariance ((mergeParam, mergeInit), resExp) (invariant, explpat', merge', resExps) =
-      (invariant, explpat', (mergeParam, mergeInit) : merge', resExp : resExps)
+            -- (1) The result is identical to the initial parameter value.
+            | mergeInit == resExp = True
+            -- (2) The initial parameter value is equal to an outer
+            -- loop parameter 'P', where the initial value of 'P' is
+            -- equal to 'resExp', AND 'resExp' ultimately becomes the
+            -- new value of 'P'.  XXX: it's a bit clumsy that this
+            -- only works for one level of nesting, and I think it
+            -- would not be too hard to generalise.
+            | Var init_v <- mergeInit,
+              Just (p_init, p_res) <- ST.lookupLoopParam init_v vtable,
+              p_init == resExp,
+              p_res == Var pat_name =
+              True
+            | otherwise = False
+    checkInvariance
+      (_pat_name, (mergeParam, mergeInit), resExp)
+      (invariant, explpat', merge', resExps) =
+        (invariant, explpat', (mergeParam, mergeInit) : merge', resExp : resExps)
 
     allExistentialInvariant namesOfInvariant mergeParam =
       all (invariantOrNotMergeParam namesOfInvariant) $
diff --git a/tests/loops/loop15.fut b/tests/loops/loop15.fut
new file mode 100644
index 0000000000..01cab0829e
--- /dev/null
+++ b/tests/loops/loop15.fut
@@ -0,0 +1,9 @@
+-- Simple case; simplify away the loops.
+-- ==
+-- input { 10 2 } output { 2 }
+-- structure { DoLoop 0 }
+
+let main (n: i32) (a: i32) =
+  loop x = a for _i < n do
+    loop _y = x for _j < n do
+      a
diff --git a/tests/loops/loop16.fut b/tests/loops/loop16.fut
new file mode 100644
index 0000000000..d4b0d64b45
--- /dev/null
+++ b/tests/loops/loop16.fut
@@ -0,0 +1,11 @@
+-- Complex case; simplify away the loops.
+-- ==
+-- input { 10 2 [1,2,3] }
+-- output { [1,2] }
+-- structure { DoLoop 0 }
+
+let main (n: i32) (a: i32) (arr: []i32) =
+  #[unsafe] -- Just to make the IR cleaner.
+  loop x = take a arr for _i < n do
+    loop _y = take (length x) arr for _j < n do
+      take a arr