diff --git a/cranelift/codegen/src/isle_prelude.rs b/cranelift/codegen/src/isle_prelude.rs
index cf0caac323b3..1d512bf386fa 100644
--- a/cranelift/codegen/src/isle_prelude.rs
+++ b/cranelift/codegen/src/isle_prelude.rs
@@ -441,6 +441,11 @@ macro_rules! isle_common_prelude_methods {
             }
         }
 
+        #[inline]
+        fn u64_is_power_of_two(&mut self, x: u64) -> bool {
+            x.is_power_of_two()
+        }
+
         #[inline]
         fn u64_from_bool(&mut self, b: bool) -> u64 {
             if b {
diff --git a/cranelift/codegen/src/opts/algebraic.isle b/cranelift/codegen/src/opts/algebraic.isle
index 3efa05dfe32e..40d5c03cf07f 100644
--- a/cranelift/codegen/src/opts/algebraic.isle
+++ b/cranelift/codegen/src/opts/algebraic.isle
@@ -59,6 +59,7 @@
       (subsume zero))
 
 ;; x/1 == x.
+;; Currently not active: see issue #5908
 (rule (simplify (sdiv ty
                       x
                       (iconst ty (u64_from_imm64 1))))
@@ -68,6 +69,17 @@
                       (iconst ty (u64_from_imm64 1))))
       (subsume x))
 
+;; x%1 == 0.
+;; Currently not active: see issue #5908
+(rule (simplify (urem ty x (iconst ty (u64_from_imm64 1))))
+      (subsume (iconst ty (imm64 0))))
+
+;; x%c == x&(c-1) when c is a power of 2.
+;; Currently not active: see issue #5908
+(rule (simplify (urem ty x (iconst ty (u64_from_imm64 c))))
+      (if-let $true (u64_is_power_of_two c))
+      (band ty x (iconst ty (imm64 (u64_sub c 1)))))
+
 ;; x>>0 == x<<0 == x rotr 0 == x rotl 0 == x.
 (rule (simplify (ishl ty
                       x
diff --git a/cranelift/codegen/src/prelude.isle b/cranelift/codegen/src/prelude.isle
index ef2741570a83..4eb772de5e46 100644
--- a/cranelift/codegen/src/prelude.isle
+++ b/cranelift/codegen/src/prelude.isle
@@ -181,6 +181,9 @@
 (decl pure u64_is_odd (u64) bool)
 (extern constructor u64_is_odd u64_is_odd)
 
+(decl pure u64_is_power_of_two (u64) bool)
+(extern constructor u64_is_power_of_two u64_is_power_of_two)
+
 ;;;; `cranelift_codegen::ir::Type` ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 
 (extern const $I8 Type)
diff --git a/cranelift/filetests/filetests/egraph/algebraic.clif b/cranelift/filetests/filetests/egraph/algebraic.clif
index faae822feb8c..c5c4815b3b5c 100644
--- a/cranelift/filetests/filetests/egraph/algebraic.clif
+++ b/cranelift/filetests/filetests/egraph/algebraic.clif
@@ -240,6 +240,24 @@ block0(v0: i32):
     ; check: return v2
 }
 
+function %urem_x_1(i32) -> i32 {
+block0(v0: i32):
+    v1 = iconst.i32 1
+    v2 = urem v0, v1
+    return v2
+    ; check: v1 = iconst.i32 1
+    ; check: v2 = urem v0, v1
+}
+
+function %urem_x_pow2(i32) -> i32 {
+block0(v0: i32):
+    v1 = iconst.i32 2
+    v2 = urem v0, v1
+    return v2
+    ; check: v1 = iconst.i32 2
+    ; check: v2 = urem v0, v1
+}
+
 function %or_and_y_with_not_y_i8(i8, i8) -> i8 {
 block0(v0: i8, v1: i8):
     v2 = band v0, v1