diff --git a/src/Futhark/Optimise/TileLoops.hs b/src/Futhark/Optimise/TileLoops.hs
index d0bf0b321a..64cd52370b 100644
--- a/src/Futhark/Optimise/TileLoops.hs
+++ b/src/Futhark/Optimise/TileLoops.hs
@@ -113,7 +113,7 @@ tileInBody branch_variant private initial_variance initial_lvl initial_space res
         not $ gtid `nameIn` branch_variant,
         (prestms', poststms') <-
           preludeToPostlude variance prestms stm_to_tile (stmsFromList poststms),
-        used <- freeIn stm_to_tile <> freeIn stms_res =
+        used <- freeIn stm_to_tile <> freeIn poststms' <> freeIn stms_res =
         Just . injectPrelude initial_space private variance prestms' used
           <$> tileGeneric
             (tiling1d $ reverse top_space_rev)
@@ -135,7 +135,7 @@ tileInBody branch_variant private initial_variance initial_lvl initial_space res
         kdim_y : kdim_x : top_kdims_rev <- reverse kdims,
         (prestms', poststms') <-
           preludeToPostlude variance prestms stm_to_tile (stmsFromList poststms),
-        used <- freeIn stm_to_tile <> freeIn stms_res =
+        used <- freeIn stm_to_tile <> freeIn poststms' <> freeIn stms_res =
         Just . injectPrelude initial_space private variance prestms' used
           <$> tileGeneric
             (tiling2d $ reverse $ zip top_gtids_rev top_kdims_rev)
diff --git a/tests/tiling/tricky_prelude0.fut b/tests/tiling/tricky_prelude0.fut
new file mode 100644
index 0000000000..edcca89456
--- /dev/null
+++ b/tests/tiling/tricky_prelude0.fut
@@ -0,0 +1,16 @@
+-- A case of tiling with a complex dependency.
+-- ==
+-- compiled random input { [100]i32 } auto output
+-- structure distributed { SegMap/DoLoop/SegMap 2 }
+
+let main (xs: []i32) =
+  map (\x ->
+         let y = x + 2 -- Used in postlude.
+         let z = loop z=0 while z < 1337 do z * 2 + y -- Uses 'y', but
+                                                      -- cannot itself
+                                                      -- be inlined in
+                                                      -- the postlude.
+         let loopres = #[sequential] i32.sum (map (+z) xs) -- Uses z.
+         in loopres + i32.clz y -- 'y' must be made available here.
+      )
+      xs