diff --git a/crates/cli-support/src/descriptor.rs b/crates/cli-support/src/descriptor.rs
index 3479a74d..09d7b332 100644
--- a/crates/cli-support/src/descriptor.rs
+++ b/crates/cli-support/src/descriptor.rs
@@ -99,6 +99,10 @@ pub enum VectorKind {
     Anyref,
 }
 
+pub struct Number {
+    u32: bool,
+}
+
 impl Descriptor {
     pub fn decode(mut data: &[u32]) -> Descriptor {
         let descriptor = Descriptor::_decode(&mut data);
@@ -149,18 +153,20 @@ impl Descriptor {
         }
     }
 
-    pub fn is_number(&self) -> bool {
+    /// Returns `Some` if this type is a number, and the returned `Number` type
+    /// can be accessed to learn more about what kind of number this is.
+    pub fn number(&self) -> Option<Number> {
         match *self {
             Descriptor::I8
             | Descriptor::U8
             | Descriptor::I16
             | Descriptor::U16
             | Descriptor::I32
-            | Descriptor::U32
             | Descriptor::F32
             | Descriptor::F64
-            | Descriptor::Enum { .. } => true,
-            _ => return false,
+            | Descriptor::Enum { .. } => Some(Number { u32: false }),
+            Descriptor::U32 => Some(Number { u32: true }),
+            _ => None,
         }
     }
 
@@ -360,3 +366,9 @@ impl VectorKind {
         }
     }
 }
+
+impl Number {
+    pub fn is_u32(&self) -> bool {
+        self.u32
+    }
+}
diff --git a/crates/cli-support/src/js/js2rust.rs b/crates/cli-support/src/js/js2rust.rs
index 61a5020d..36f3fe08 100644
--- a/crates/cli-support/src/js/js2rust.rs
+++ b/crates/cli-support/src/js/js2rust.rs
@@ -384,7 +384,7 @@ impl<'a, 'b> Js2Rust<'a, 'b> {
             return Ok(self);
         }
 
-        if arg.is_number() {
+        if arg.number().is_some() {
             self.js_arguments.push((name.clone(), "number".to_string()));
 
             if self.cx.config.debug {
@@ -681,9 +681,13 @@ impl<'a, 'b> Js2Rust<'a, 'b> {
             return Ok(self);
         }
 
-        if ty.is_number() {
+        if let Some(num) = ty.number() {
             self.ret_ty = "number".to_string();
-            self.ret_expr = format!("return RET;");
+            if num.is_u32() {
+                self.ret_expr = format!("return RET >>> 0;");
+            } else {
+                self.ret_expr = format!("return RET;");
+            }
             return Ok(self);
         }
 
diff --git a/crates/cli-support/src/js/rust2js.rs b/crates/cli-support/src/js/rust2js.rs
index b5d68ddf..8e706dec 100644
--- a/crates/cli-support/src/js/rust2js.rs
+++ b/crates/cli-support/src/js/rust2js.rs
@@ -309,8 +309,16 @@ impl<'a, 'b> Rust2Js<'a, 'b> {
             return Ok(());
         }
 
+        if let Some(num) = arg.number() {
+            if num.is_u32() {
+                self.js_arguments.push(format!("{} >>> 0", abi));
+            } else {
+                self.js_arguments.push(abi);
+            }
+            return Ok(());
+        }
+
         let invoc_arg = match *arg {
-            ref d if d.is_number() => abi,
             Descriptor::Boolean => format!("{} !== 0", abi),
             Descriptor::Char => format!("String.fromCodePoint({})", abi),
             _ => bail!(
@@ -504,7 +512,7 @@ impl<'a, 'b> Rust2Js<'a, 'b> {
 
             return Ok(());
         }
-        if ty.is_number() {
+        if ty.number().is_some() {
             self.ret_expr = "return JS;".to_string();
             return Ok(());
         }
diff --git a/tests/wasm/math.js b/tests/wasm/math.js
index c4865494..e3b51830 100644
--- a/tests/wasm/math.js
+++ b/tests/wasm/math.js
@@ -1,5 +1,37 @@
 const wasm = require('wasm-bindgen-test.js');
+const assert = require('assert');
 
 exports.js_auto_bind_math = () => {
     wasm.math(1.0, 2.0);
 };
+
+exports.roundtrip = x => x;
+
+exports.test_js_roundtrip = () => {
+  assert.strictEqual(wasm.rust_roundtrip_i8(0), 0);
+  assert.strictEqual(wasm.rust_roundtrip_i8(0x80), -128);
+  assert.strictEqual(wasm.rust_roundtrip_i8(0x7f), 127);
+
+  assert.strictEqual(wasm.rust_roundtrip_i16(0), 0);
+  assert.strictEqual(wasm.rust_roundtrip_i16(0x8000), -32768);
+  assert.strictEqual(wasm.rust_roundtrip_i16(0x7fff), 32767);
+
+  assert.strictEqual(wasm.rust_roundtrip_i32(0), 0);
+  assert.strictEqual(wasm.rust_roundtrip_i32(0x80000000), -2147483648);
+  assert.strictEqual(wasm.rust_roundtrip_i32(0x7fffffff), 2147483647);
+
+  assert.strictEqual(wasm.rust_roundtrip_u8(0), 0);
+  assert.strictEqual(wasm.rust_roundtrip_u8(0x80), 128);
+  assert.strictEqual(wasm.rust_roundtrip_u8(0x7f), 127);
+  assert.strictEqual(wasm.rust_roundtrip_u8(0xff), 255);
+
+  assert.strictEqual(wasm.rust_roundtrip_u16(0), 0);
+  assert.strictEqual(wasm.rust_roundtrip_u16(0x8000), 32768);
+  assert.strictEqual(wasm.rust_roundtrip_u16(0x7fff), 32767);
+  assert.strictEqual(wasm.rust_roundtrip_u16(0xffff), 65535);
+
+  assert.strictEqual(wasm.rust_roundtrip_u32(0), 0);
+  assert.strictEqual(wasm.rust_roundtrip_u32(0x80000000), 2147483648);
+  assert.strictEqual(wasm.rust_roundtrip_u32(0x7fffffff), 2147483647);
+  assert.strictEqual(wasm.rust_roundtrip_u32(0xffffffff), 4294967295);
+};
diff --git a/tests/wasm/math.rs b/tests/wasm/math.rs
index 90d3fa85..ba5b799f 100644
--- a/tests/wasm/math.rs
+++ b/tests/wasm/math.rs
@@ -4,6 +4,26 @@ use wasm_bindgen_test::*;
 #[wasm_bindgen(module = "tests/wasm/math.js")]
 extern "C" {
     fn js_auto_bind_math();
+
+    // There's an identity function called `roundtrip` in the module and we bind
+    // that one function with multiple different signatures here. Note that the
+    // return value is always `f64` to faithfully capture what was sent to JS
+    // (what we're interested in) because all JS numbers fit in `f64` anyway.
+    // This is testing what happens when we pass numbers to JS and what it sees.
+    #[wasm_bindgen(js_name = roundtrip)]
+    fn roundtrip_i8(a: i8) -> f64;
+    #[wasm_bindgen(js_name = roundtrip)]
+    fn roundtrip_i16(a: i16) -> f64;
+    #[wasm_bindgen(js_name = roundtrip)]
+    fn roundtrip_i32(a: i32) -> f64;
+    #[wasm_bindgen(js_name = roundtrip)]
+    fn roundtrip_u8(a: u8) -> f64;
+    #[wasm_bindgen(js_name = roundtrip)]
+    fn roundtrip_u16(a: u16) -> f64;
+    #[wasm_bindgen(js_name = roundtrip)]
+    fn roundtrip_u32(a: u32) -> f64;
+
+    fn test_js_roundtrip();
 }
 
 #[wasm_bindgen]
@@ -65,3 +85,44 @@ pub fn math(a: f32, b: f64) -> f64 {
 fn auto_bind_math() {
     js_auto_bind_math();
 }
+
+macro_rules! t_roundtrip {
+    ($f:ident($e:expr)) => (assert_eq!($f($e), $e as f64))
+}
+
+#[wasm_bindgen_test]
+fn limits_correct() {
+    t_roundtrip!(roundtrip_i8(i8::min_value()));
+    t_roundtrip!(roundtrip_i8(0));
+    t_roundtrip!(roundtrip_i8(i8::max_value()));
+    t_roundtrip!(roundtrip_i16(i16::min_value()));
+    t_roundtrip!(roundtrip_i16(0));
+    t_roundtrip!(roundtrip_i16(i16::max_value()));
+    t_roundtrip!(roundtrip_i32(i32::min_value()));
+    t_roundtrip!(roundtrip_i32(0));
+    t_roundtrip!(roundtrip_i32(i32::max_value()));
+    t_roundtrip!(roundtrip_u8(u8::min_value()));
+    t_roundtrip!(roundtrip_u8(0));
+    t_roundtrip!(roundtrip_u8(u8::max_value()));
+    t_roundtrip!(roundtrip_u16(u16::min_value()));
+    t_roundtrip!(roundtrip_u16(0));
+    t_roundtrip!(roundtrip_u16(u16::max_value()));
+    t_roundtrip!(roundtrip_u32(u32::min_value()));
+    t_roundtrip!(roundtrip_u32(0));
+    t_roundtrip!(roundtrip_u32(u32::max_value()));
+
+    test_js_roundtrip();
+
+    #[wasm_bindgen]
+    pub fn rust_roundtrip_i8(a: i8) -> i8 { a }
+    #[wasm_bindgen]
+    pub fn rust_roundtrip_i16(a: i16) -> i16 { a }
+    #[wasm_bindgen]
+    pub fn rust_roundtrip_i32(a: i32) -> i32 { a }
+    #[wasm_bindgen]
+    pub fn rust_roundtrip_u8(a: u8) -> u8 { a }
+    #[wasm_bindgen]
+    pub fn rust_roundtrip_u16(a: u16) -> u16 { a }
+    #[wasm_bindgen]
+    pub fn rust_roundtrip_u32(a: u32) -> u32 { a }
+}