diff --git a/CHANGELOG.md b/CHANGELOG.md
index ea8971b62d..d6bc198343 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -32,6 +32,9 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 * Error in type checking of horisontally fused `scatter`s could crash
   the compiler (#2009).
 
+* Size-polymorphic value bindings with existential sizes are now
+  rejected by type checker (#1993).
+
 ## [0.25.2]
 
 ### Added
diff --git a/src/Language/Futhark/TypeChecker/Terms.hs b/src/Language/Futhark/TypeChecker/Terms.hs
index 54a2d0e7cf..195ca81c2d 100644
--- a/src/Language/Futhark/TypeChecker/Terms.hs
+++ b/src/Language/Futhark/TypeChecker/Terms.hs
@@ -1480,6 +1480,18 @@ checkBinding (fname, maybe_retdecl, tparams, params, body, loc) =
       letGeneralise fname loc tparams' params''
         =<< unscopeUnknown rettype
 
+    when
+      ( null params
+          && any isSizeParam tparams''
+          && not (null (retDims rettype'))
+      )
+      $ typeError loc mempty
+      $ textwrap "A size-polymorphic value binding may not have a type with an existential size."
+        </> "Type of this binding is:"
+        </> indent 2 (pretty rettype')
+        </> "with the following type parameters:"
+        </> indent 2 (sep $ map pretty $ filter isSizeParam tparams'')
+
     pure (tparams'', params''', maybe_retdecl'', rettype', body')
 
 -- | Extract all the shape names that occur in positive position
diff --git a/tests/shapes/toplevel2.fut b/tests/shapes/toplevel2.fut
new file mode 100644
index 0000000000..1aea78c37f
--- /dev/null
+++ b/tests/shapes/toplevel2.fut
@@ -0,0 +1,6 @@
+-- #1993, do not allow size-polymorphic non-function bindings with
+-- unknown sizes.
+-- ==
+-- error: size-polymorphic value binding
+
+def foo [n] = (iota n, filter (>5) (iota n))