diff --git a/kernel/bpf/verifier.c b/kernel/bpf/verifier.c
index 8574cb6..94ba516 100644
--- a/kernel/bpf/verifier.c
+++ b/kernel/bpf/verifier.c
@@ -6545,8 +6545,12 @@ static int sanitize_ptr_alu(struct bpf_verifier_env *env,
 	/* If we're in commit phase, we're done here given we already
 	 * pushed the truncated dst_reg into the speculative verification
 	 * stack.
+	 *
+	 * Also, when register is a known constant, we rewrite register-based
+	 * operation to immediate-based, and thus do not need masking (and as
+	 * a consequence, do not need to simulate the zero-truncation either).
 	 */
-	if (commit_window)
+	if (commit_window || off_is_imm)
 		return 0;
 
 	/* Simulate and find potential out-of-bounds access under