diff --git a/cranelift/codegen/src/opts/algebraic.isle b/cranelift/codegen/src/opts/algebraic.isle
index 061c61c511..e0f7fc4654 100644
--- a/cranelift/codegen/src/opts/algebraic.isle
+++ b/cranelift/codegen/src/opts/algebraic.isle
@@ -289,3 +289,47 @@
 (rule (simplify (bxor ty x (iconst ty k)))
   (if-let -1 (i64_sextend_imm64 ty k))
   (bnot ty x))
+
+
+;; Masking the result of a comparison with 1 always results in the comparison
+;; itself. Note that comparisons in wasm may sometimes be hidden behind
+;; extensions.
+(rule (simplify
+       (band (ty_int _)
+             cmp @ (icmp _ _ _ _)
+             (iconst _ (u64_from_imm64 1))))
+      cmp)
+(rule (simplify
+       (band (ty_int _)
+             extend @ (uextend _ (icmp _ _ _ _))
+             (iconst _ (u64_from_imm64 1))))
+      extend)
+
+;; `x < 0` is always false for unsigned integers, and `x >= 0` is always true
+;; for unsigned integers, along with their reversals.
+(rule (simplify
+       (icmp (fits_in_64 (ty_int ty))
+             (IntCC.UnsignedLessThan)
+             _
+             (iconst _ (u64_from_imm64 0))))
+      (iconst ty (imm64 0)))
+(rule (simplify
+       (icmp (fits_in_64 (ty_int ty))
+             (IntCC.UnsignedGreaterThanOrEqual)
+             _
+             (iconst _ (u64_from_imm64 0))))
+      (iconst ty (imm64 1)))
+
+;; 32-bit integers zero-extended to 64-bit integers are never negative
+(rule (simplify
+       (icmp (ty_int ty)
+             (IntCC.SignedLessThan)
+             (uextend $I64 x @ (value_type $I32))
+             (iconst _ (u64_from_imm64 0))))
+      (iconst ty (imm64 0)))
+(rule (simplify
+       (icmp (ty_int ty)
+             (IntCC.SignedGreaterThanOrEqual)
+             (uextend $I64 x @ (value_type $I32))
+             (iconst _ (u64_from_imm64 0))))
+      (iconst ty (imm64 1)))
diff --git a/cranelift/codegen/src/opts/cprop.isle b/cranelift/codegen/src/opts/cprop.isle
index 817bffcd98..f0def3acca 100644
--- a/cranelift/codegen/src/opts/cprop.isle
+++ b/cranelift/codegen/src/opts/cprop.isle
@@ -110,6 +110,10 @@
        (bxor ty k @ (iconst ty _) x))
       (bxor ty x k))
 
+(rule (simplify
+       (icmp ty cc k @ (iconst _ _) x))
+      (icmp ty (intcc_reverse cc) x k))
+
 ;; Canonicalize via associativity: reassociate to a right-heavy tree
 ;; for constants.
 ;;
diff --git a/cranelift/filetests/filetests/egraph/algebraic.clif b/cranelift/filetests/filetests/egraph/algebraic.clif
index 1962eb508f..af8062d6ad 100644
--- a/cranelift/filetests/filetests/egraph/algebraic.clif
+++ b/cranelift/filetests/filetests/egraph/algebraic.clif
@@ -251,3 +251,89 @@ block0(v1: i64):
 
 ; check: v5 = bnot v1
 ; check: return v5
+
+function %mask_icmp_result(i64, i64) -> i8 {
+block0(v1: i64, v2: i64):
+    v3 = icmp ult v1, v2
+    v4 = iconst.i8 1
+    v5 = band v3, v4
+    return v5
+}
+
+; check: v3 = icmp ult v1, v2
+; check: return v3
+
+function %mask_icmp_extend_result(i64, i64) -> i64 {
+block0(v1: i64, v2: i64):
+    v3 = icmp ult v1, v2
+    v4 = uextend.i64 v3
+    v5 = iconst.i64 1
+    v6 = band v4, v5
+    return v6
+}
+
+; check: v3 = icmp ult v1, v2
+; check: v4 = uextend.i64 v3
+; check: return v4
+
+function %ult_zero_always_false(i64) -> i8 {
+block0(v1: i64):
+    v2 = iconst.i64 0
+    v3 = icmp ult v1, v2
+    return v3
+}
+
+; check: v4 = iconst.i8 0
+; check: return v4
+
+function %ugt_zero_always_false(i64) -> i8 {
+block0(v1: i64):
+    v2 = iconst.i64 0
+    v3 = icmp ugt v2, v1
+    return v3
+}
+
+; check: v5 = iconst.i8 0
+; check: return v5
+
+function %uge_zero_always_false(i64) -> i8 {
+block0(v1: i64):
+    v2 = iconst.i64 0
+    v3 = icmp uge v1, v2
+    return v3
+}
+
+; check: v4 = iconst.i8 1
+; check: return v4
+
+function %ule_zero_always_false(i64) -> i8 {
+block0(v1: i64):
+    v2 = iconst.i64 0
+    v3 = icmp ule v2, v1
+    return v3
+}
+
+; check: v5 = iconst.i8 1
+; check: return v5
+
+function %extend_always_above_zero(i32) -> i8 {
+block0(v1: i32):
+    v2 = uextend.i64 v1
+    v3 = iconst.i64 0
+    v4 = icmp slt v2, v3
+    return v4
+}
+
+; check: v5 = iconst.i8 0
+; check: return v5
+
+function %extend_always_above_zero2(i32) -> i8 {
+block0(v1: i32):
+    v2 = uextend.i64 v1
+    v3 = iconst.i64 0
+    v4 = icmp sge v2, v3
+    return v4
+}
+
+; check: v5 = iconst.i8 1
+; check: return v5