diff --git a/docs/language-reference.rst b/docs/language-reference.rst
index 6c926b9376..d29419eb58 100644
--- a/docs/language-reference.rst
+++ b/docs/language-reference.rst
@@ -936,6 +936,10 @@ is optional if ``body`` is a ``let`` expression.  The binding is not
 let-generalised, meaning it has a monomorphic type.  This can be
 significant if ``e`` is of functional type.
 
+If ``e`` is of type ``i64`` and ``pat`` binds only a single name
+``v``, then the type of the overall expression is the type of
+``body``, but with any occurence of ``v`` replaced by ``e``.
+
 ``let [n] pat = e in body``
 ...........................
 
@@ -1156,11 +1160,11 @@ sizes.
 Size going out of scope
 .......................
 
-An unknown size is created when the proper size of an array refers to
-a name that has gone out of scope::
+An unknown size is created in some cases when the a type references a
+name that has gone out of scope::
 
-  let c = a + b
-  in replicate c 0
+  match ...
+  case #some c -> replicate c 0
 
 The type of ``replicate c 0`` is ``[c]i32``, but since ``c`` is
 locally bound, the type of the entire expression is ``[k]i32`` for
diff --git a/src/Language/Futhark/TypeChecker/Terms.hs b/src/Language/Futhark/TypeChecker/Terms.hs
index a444b9d0d7..9e7e9ff110 100644
--- a/src/Language/Futhark/TypeChecker/Terms.hs
+++ b/src/Language/Futhark/TypeChecker/Terms.hs
@@ -610,7 +610,20 @@ checkExp (AppExp (LetPat sizes pat e body loc) _) = do
     bindingPat sizes' pat t $ \pat' -> do
       body' <- checkExp body
       body_t <- expTypeFully body'
-      (body_t', retext) <- unscopeType loc (patNames pat') body_t
+
+      -- If the bound expression is of type i64, then we replace the
+      -- pattern name with the expression in the type of the body.
+      -- Otherwise, we need to come up with unknown sizes for the
+      -- sizes going out of scope.
+      t' <- normType t -- Might be overloaded integer until now.
+      (body_t', retext) <-
+        case (t', patNames pat') of
+          (Scalar (Prim (Signed Int64)), [v])
+            | not $ hasBinding e' -> do
+                let f x = if x == v then Just (ExpSubst e') else Nothing
+                pure (applySubst f body_t, [])
+          _ ->
+            unscopeType loc (patNames pat') body_t
 
       pure $
         AppExp
diff --git a/tests/returntype-error4.fut b/tests/returntype-error4.fut
index 013cbb4494..15525e522f 100644
--- a/tests/returntype-error4.fut
+++ b/tests/returntype-error4.fut
@@ -2,7 +2,7 @@
 -- error: Cannot generalise
 
 def foo n =
-  let m = n+1
+  let (m,_) = (n+1,true)
   in (iota ((m+1)+1),
       zip (iota (m+1)),
       zip (iota m))
diff --git a/tests/shapes/letshape5.fut b/tests/shapes/letshape5.fut
index 2a4f39b5cd..568fe1944e 100644
--- a/tests/shapes/letshape5.fut
+++ b/tests/shapes/letshape5.fut
@@ -1,7 +1,8 @@
 -- A size goes out of scope.
 -- ==
--- error: "m"
+-- input { 2i64 }
+-- output { [0i64,1i64,2i64] }
 
-def main (n: i64) : [n]i32 =
-  let m = n
+def main (n: i64) : [n+1]i64 =
+  let m = n + 1
   in iota m
diff --git a/tests/shapes/unknown-param.fut b/tests/shapes/unknown-param.fut
index 971e9dfb71..5175c9c9d9 100644
--- a/tests/shapes/unknown-param.fut
+++ b/tests/shapes/unknown-param.fut
@@ -4,5 +4,5 @@
 -- error: Unknown size.*in parameter
 
 def f (x: bool) =
-  let n = if x then 10 else 20
+  let (n,_) = if x then (10,true) else (20,true)
   in \(_: [n]bool) -> true
diff --git a/tests/sumtypes/sumtype51.fut b/tests/sumtypes/sumtype51.fut
index ec5dceb0cc..c782f18f09 100644
--- a/tests/sumtypes/sumtype51.fut
+++ b/tests/sumtypes/sumtype51.fut
@@ -5,7 +5,7 @@
 type option 'a = #None | #Some a
 
 def gen () : ?[n].[n]i32 =
-  let n = 0
+  let (n,_) = (0,true)
   in replicate n 0i32
 
 entry main b: option ([]i32) =
diff --git a/tests/sumtypes/sumtype52.fut b/tests/sumtypes/sumtype52.fut
index c9acdffcdd..1ed6fca70d 100644
--- a/tests/sumtypes/sumtype52.fut
+++ b/tests/sumtypes/sumtype52.fut
@@ -5,7 +5,7 @@
 type option 'a = #None | #Some a
 
 def gen () : ?[n].[n]i32 =
-  let n = 0
+  let (n,_) = (0,true)
   in replicate n 0i32
 
 def ite b t f = if b then t() else f()
diff --git a/tests/unscoping.fut b/tests/unscoping.fut
index d11fc0f29f..903b06d874 100644
--- a/tests/unscoping.fut
+++ b/tests/unscoping.fut
@@ -2,7 +2,7 @@
 -- error: Cannot apply "bar" to "xs"
 
 def foo n =
-  let m = n+1
+  let (m,_) = (n+1,true)
   in (iota ((m+1)+1),
       \_ -> iota (m+1),
       \_ -> iota m)