diff --git a/src/uint/modular/constant_mod.rs b/src/uint/modular/constant_mod.rs
index 92b6ce761..b775af45b 100644
--- a/src/uint/modular/constant_mod.rs
+++ b/src/uint/modular/constant_mod.rs
@@ -1,6 +1,6 @@
 use core::{fmt::Debug, marker::PhantomData};
 
-use subtle::{Choice, ConditionallySelectable, ConstantTimeEq};
+use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 
 use crate::{Limb, Uint, Zero};
 
@@ -87,8 +87,8 @@ impl<MOD: ResidueParams<LIMBS>, const LIMBS: usize> Residue<MOD, LIMBS> {
         phantom: PhantomData,
     };
 
-    /// Instantiates a new `Residue` that represents this `integer` mod `MOD`.
-    pub const fn new(integer: &Uint<LIMBS>) -> Self {
+    // Internal helper function to generate a residue; this lets us wrap the constructors more cleanly
+    const fn generate_residue(integer: &Uint<LIMBS>) -> Self {
         let product = integer.mul_wide(&MOD::R2);
         let montgomery_form =
             montgomery_reduction::<LIMBS>(&product, &MOD::MODULUS, MOD::MOD_NEG_INV);
@@ -99,6 +99,29 @@ impl<MOD: ResidueParams<LIMBS>, const LIMBS: usize> Residue<MOD, LIMBS> {
         }
     }
 
+    /// Instantiates a new `Residue` that represents this `integer` mod `MOD`.
+    /// If the modulus represented by `MOD` is not odd, this function will panic; use [`new_checked`][`Residue::new_checked`] if you want to be able to detect an invalid modulus.
+    pub const fn new(integer: &Uint<LIMBS>) -> Self {
+        // A valid modulus must be odd
+        if MOD::MODULUS.ct_is_odd().to_u8() == 0 {
+            panic!("modulus must be odd");
+        }
+
+        Self::generate_residue(integer)
+    }
+
+    /// Instantiates a new `Residue` that represents this `integer` mod `MOD` if the modulus is odd.
+    /// Returns a `CtOption` that is `None` if the provided modulus is not odd; this is a safer version of [`new`][`Residue::new`], which can panic.
+    // TODO: remove this method when we can use `generic_const_exprs.` to ensure the modulus is
+    // always valid.
+    pub fn new_checked(integer: &Uint<LIMBS>) -> CtOption<Self> {
+        // A valid modulus must be odd, which we can check in constant time
+        CtOption::new(
+            Self::generate_residue(integer),
+            MOD::MODULUS.ct_is_odd().into(),
+        )
+    }
+
     /// Retrieves the integer currently encoded in this `Residue`, guaranteed to be reduced.
     pub const fn retrieve(&self) -> Uint<LIMBS> {
         montgomery_reduction::<LIMBS>(
diff --git a/src/uint/modular/constant_mod/macros.rs b/src/uint/modular/constant_mod/macros.rs
index 1583ca529..70dc4379d 100644
--- a/src/uint/modular/constant_mod/macros.rs
+++ b/src/uint/modular/constant_mod/macros.rs
@@ -2,6 +2,7 @@
 #[macro_export]
 /// Implements a modulus with the given name, type, and value, in that specific order. Please `use crypto_bigint::traits::Encoding` to make this work.
 /// For example, `impl_modulus!(MyModulus, U256, "73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001");` implements a 256-bit modulus named `MyModulus`.
+/// The modulus _must_ be odd, or this will panic.
 macro_rules! impl_modulus {
     ($name:ident, $uint_type:ty, $value:expr) => {
         #[derive(Clone, Copy, Debug, Default, Eq, PartialEq)]
@@ -14,8 +15,16 @@ macro_rules! impl_modulus {
                 $crate::Concat<Output = $crate::Uint<DLIMBS>>,
         {
             const LIMBS: usize = { $crate::nlimbs!(<$uint_type>::BITS) };
-            const MODULUS: $crate::Uint<{ $crate::nlimbs!(<$uint_type>::BITS) }> =
-                <$uint_type>::from_be_hex($value);
+            const MODULUS: $crate::Uint<{ $crate::nlimbs!(<$uint_type>::BITS) }> = {
+                let res = <$uint_type>::from_be_hex($value);
+
+                // Check that the modulus is odd
+                if res.as_limbs()[0].0 & 1 == 0 {
+                    panic!("modulus must be odd");
+                }
+
+                res
+            };
             const R: $crate::Uint<{ $crate::nlimbs!(<$uint_type>::BITS) }> = $crate::Uint::MAX
                 .const_rem(&Self::MODULUS)
                 .0
@@ -43,6 +52,7 @@ macro_rules! impl_modulus {
 #[macro_export]
 /// Creates a `Residue` with the given value for a specific modulus.
 /// For example, `residue!(U256::from(105u64), MyModulus);` creates a `Residue` for 105 mod `MyModulus`.
+/// The modulus _must_ be odd, or this will panic.
 macro_rules! const_residue {
     ($variable:ident, $modulus:ident) => {
         $crate::modular::constant_mod::Residue::<$modulus, { $modulus::LIMBS }>::new(&$variable)