diff --git a/src/uint/modular/runtime_mod.rs b/src/uint/modular/runtime_mod.rs
index 32b078599..4468d71ac 100644
--- a/src/uint/modular/runtime_mod.rs
+++ b/src/uint/modular/runtime_mod.rs
@@ -7,6 +7,8 @@ use super::{
     Retrieve,
 };
 
+use subtle::CtOption;
+
 /// Additions between residues with a modulus set at runtime
 mod runtime_add;
 /// Multiplicative inverses of residues with a modulus set at runtime
@@ -20,7 +22,7 @@ mod runtime_pow;
 /// Subtractions between residues with a modulus set at runtime
 mod runtime_sub;
 
-/// The parameters to efficiently go to and from the Montgomery form for a modulus provided at runtime.
+/// The parameters to efficiently go to and from the Montgomery form for an odd modulus provided at runtime.
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
 pub struct DynResidueParams<const LIMBS: usize> {
     // The constant modulus
@@ -37,8 +39,8 @@ pub struct DynResidueParams<const LIMBS: usize> {
 }
 
 impl<const LIMBS: usize> DynResidueParams<LIMBS> {
-    /// Instantiates a new set of `ResidueParams` representing the given `modulus`.
-    pub const fn new(modulus: &Uint<LIMBS>) -> Self {
+    // Internal helper function to generate parameters; this lets us wrap the constructors more cleanly
+    const fn generate_params(modulus: &Uint<LIMBS>) -> Self {
         let r = Uint::MAX.const_rem(modulus).0.wrapping_add(&Uint::ONE);
         let r2 = Uint::const_rem_wide(r.square_wide(), modulus).0;
 
@@ -59,6 +61,28 @@ impl<const LIMBS: usize> DynResidueParams<LIMBS> {
         }
     }
 
+    /// Instantiates a new set of `ResidueParams` representing the given `modulus`, which _must_ be odd.
+    /// If `modulus` is not odd, this function will panic; use [`new_checked`][`DynResidueParams::new_checked`] if you want to be able to detect an invalid modulus.
+    pub const fn new(modulus: &Uint<LIMBS>) -> Self {
+        // A valid modulus must be odd
+        if modulus.ct_is_odd().to_u8() == 0 {
+            panic!("modulus must be odd");
+        }
+
+        Self::generate_params(modulus)
+    }
+
+    /// Instantiates a new set of `ResidueParams` representing the given `modulus` if it is odd.
+    /// Returns a `CtOption` that is `None` if the provided modulus is not odd; this is a safer version of [`new`][`DynResidueParams::new`], which can panic.
+    #[deprecated(
+        since = "0.5.3",
+        note = "This functionality will be moved to `new` in a future release."
+    )]
+    pub fn new_checked(modulus: &Uint<LIMBS>) -> CtOption<Self> {
+        // A valid modulus must be odd, which we check in constant time
+        CtOption::new(Self::generate_params(modulus), modulus.ct_is_odd().into())
+    }
+
     /// Returns the modulus which was used to initialize these parameters.
     pub const fn modulus(&self) -> &Uint<LIMBS> {
         &self.modulus
@@ -194,3 +218,37 @@ impl<const LIMBS: usize> zeroize::Zeroize for DynResidue<LIMBS> {
         self.montgomery_form.zeroize()
     }
 }
+
+#[cfg(test)]
+mod test {
+    use super::*;
+    use crate::nlimbs;
+
+    const LIMBS: usize = nlimbs!(64);
+
+    #[test]
+    #[allow(deprecated)]
+    // Test that a valid modulus yields `DynResidueParams`
+    fn test_valid_modulus() {
+        let valid_modulus = Uint::<LIMBS>::from(3u8);
+
+        DynResidueParams::<LIMBS>::new_checked(&valid_modulus).unwrap();
+        DynResidueParams::<LIMBS>::new(&valid_modulus);
+    }
+
+    #[test]
+    #[allow(deprecated)]
+    // Test that an invalid checked modulus does not yield `DynResidueParams`
+    fn test_invalid_checked_modulus() {
+        assert!(bool::from(
+            DynResidueParams::<LIMBS>::new_checked(&Uint::from(2u8)).is_none()
+        ))
+    }
+
+    #[test]
+    #[should_panic]
+    // Tets that an invalid modulus panics
+    fn test_invalid_modulus() {
+        DynResidueParams::<LIMBS>::new(&Uint::from(2u8));
+    }
+}