diff --git a/compiler/basicTypes/MkId.hs b/compiler/basicTypes/MkId.hs
index c6161c52cda79c0346b72a4f9a14d6bdd775d11b..c3a9f9a7c82f03783fc7d6c63bb05dbf1e2ff740 100644
--- a/compiler/basicTypes/MkId.hs
+++ b/compiler/basicTypes/MkId.hs
@@ -941,8 +941,11 @@ mkFCallId dflags uniq fcall ty
     (_, tau)        = tcSplitForAllTys ty
     (arg_tys, _)    = tcSplitFunTys tau
     arity           = length arg_tys
-    strict_sig      = mkClosedStrictSig (replicate arity evalDmd) topRes
 
+    strict_sig      = mkClosedStrictSig (replicate arity topDmd) topRes
+    -- the call does not claim to be strict in its arguments, since they
+    -- may be lifted (foreign import prim) and the called code doen't
+    -- necessarily force them. See Trac #11076.
 {-
 ************************************************************************
 *                                                                      *
diff --git a/testsuite/tests/stranal/should_run/T11076.hs b/testsuite/tests/stranal/should_run/T11076.hs
new file mode 100644
index 0000000000000000000000000000000000000000..f095cc1ff886dbd9b774a31ef8d95f90cabf67de
--- /dev/null
+++ b/testsuite/tests/stranal/should_run/T11076.hs
@@ -0,0 +1,15 @@
+{-
+   Test case for a problem where GHC had incorrect strictness
+   information for foreign calls with lifted arguments
+ -}
+{-# OPTIONS_GHC -O0 #-}
+module Main where
+
+import T11076A
+import Control.Exception
+x :: Bool
+x = error "OK: x has been forced"
+
+main :: IO ()
+main = print (testBool x) `catch`
+          \(ErrorCall e) -> putStrLn e -- x should be forced
diff --git a/testsuite/tests/stranal/should_run/T11076.stdout b/testsuite/tests/stranal/should_run/T11076.stdout
new file mode 100644
index 0000000000000000000000000000000000000000..8a17d8b29b6dda4a0b1cb3254960513ec620bec8
--- /dev/null
+++ b/testsuite/tests/stranal/should_run/T11076.stdout
@@ -0,0 +1 @@
+OK: x has been forced
diff --git a/testsuite/tests/stranal/should_run/T11076A.hs b/testsuite/tests/stranal/should_run/T11076A.hs
new file mode 100644
index 0000000000000000000000000000000000000000..153a887ef6c8e891684ab79e6d0b46e93a7103b1
--- /dev/null
+++ b/testsuite/tests/stranal/should_run/T11076A.hs
@@ -0,0 +1,21 @@
+{-# OPTIONS_GHC -O #-}
+{-# LANGUAGE MagicHash,
+             ForeignFunctionInterface,
+             UnliftedFFITypes,
+             GHCForeignImportPrim,
+             BangPatterns
+  #-}
+module T11076A where
+
+import GHC.Exts
+import Unsafe.Coerce
+
+{-
+   If the demand type for the foreign call argument is incorrectly strict,
+   the bang pattern can be optimized out
+ -}
+testBool :: Bool -> Int
+testBool !x = I# (cmm_testPrim (unsafeCoerce x))
+{-# INLINE testBool #-}
+
+foreign import prim "testPrim" cmm_testPrim :: Any -> Int#
diff --git a/testsuite/tests/stranal/should_run/T11076_prim.cmm b/testsuite/tests/stranal/should_run/T11076_prim.cmm
new file mode 100644
index 0000000000000000000000000000000000000000..6e738a78a17880f60e2d4e6f482d2fcfc5580acf
--- /dev/null
+++ b/testsuite/tests/stranal/should_run/T11076_prim.cmm
@@ -0,0 +1,10 @@
+#include "Cmm.h"
+#include "MachDeps.h"
+
+testPrim(gcptr x)
+{
+  W_ a;
+  a = 123;
+  return (a);
+}
+
diff --git a/testsuite/tests/stranal/should_run/all.T b/testsuite/tests/stranal/should_run/all.T
index 8a82ce86a5a15759f457a03a888d3daf03f7feea..efd1afaa353a941d5c68f758b5415ff51f4fd65e 100644
--- a/testsuite/tests/stranal/should_run/all.T
+++ b/testsuite/tests/stranal/should_run/all.T
@@ -10,3 +10,4 @@ test('T7649', normal, compile_and_run, [''])
 test('T9254', normal, compile_and_run, [''])
 test('T10148', normal, compile_and_run, [''])
 test('T10218', normal, compile_and_run, [''])
+test('T11076', normal, multimod_compile_and_run, ['T11076.hs', 'T11076_prim.cmm'])
diff --git a/testsuite/tests/stranal/sigs/T8598.stderr b/testsuite/tests/stranal/sigs/T8598.stderr
index 8de5d31a01db8fa8be08d005bd1b7518bcce268c..a457cc5f507e15b79d8d1dd2d74478a832bba1bd 100644
--- a/testsuite/tests/stranal/sigs/T8598.stderr
+++ b/testsuite/tests/stranal/sigs/T8598.stderr
@@ -1,5 +1,5 @@
 
 ==================== Strictness signatures ====================
-T8598.fun: <S(S),1*U(U)>m
+T8598.fun: <S,1*U(U)>m