diff --git a/src/generic.rs b/src/generic.rs
index dd08d6c..fc55b2c 100644
--- a/src/generic.rs
+++ b/src/generic.rs
@@ -8,9 +8,13 @@ use crate::SieveFactory;
 /// Sieves through the results of `sieve_factory` and returns the first item for which `predicate` is `true`.
 ///
 /// If `sieve_factory` signals that no more results can be created, returns `None`.
-pub fn sieve_and_find<R, S, T>(rng: &mut R, sieve_factory: S, predicate: impl Fn(&mut R, &T) -> bool) -> Option<T>
+pub fn sieve_and_find<R, S>(
+    rng: &mut R,
+    sieve_factory: S,
+    predicate: impl Fn(&mut R, &S::Item) -> bool,
+) -> Option<S::Item>
 where
-    S: SieveFactory<T>,
+    S: SieveFactory,
     R: CryptoRngCore,
 {
     // We could use `SieveIterator` here, but it requires cloning the `rng`.
@@ -63,13 +67,13 @@ where
 /// A structure that chains the creation of sieves, returning the results from one until it is exhausted,
 /// and then creating a new one.
 #[derive(Debug)]
-pub struct SieveIterator<'a, R: CryptoRngCore, T, S: SieveFactory<T>> {
+pub struct SieveIterator<'a, R: CryptoRngCore, S: SieveFactory> {
     sieve_factory: S,
     sieve: S::Sieve,
     rng: &'a mut R,
 }
 
-impl<'a, R: CryptoRngCore, T, S: SieveFactory<T>> SieveIterator<'a, R, T, S> {
+impl<'a, R: CryptoRngCore, S: SieveFactory> SieveIterator<'a, R, S> {
     /// Creates a new chained iterator producing results from sieves returned from `sieve_factory`.
     pub fn new(rng: &'a mut R, sieve_factory: S) -> Option<Self> {
         let mut sieve_factory = sieve_factory;
@@ -82,8 +86,8 @@ impl<'a, R: CryptoRngCore, T, S: SieveFactory<T>> SieveIterator<'a, R, T, S> {
     }
 }
 
-impl<'a, R: CryptoRngCore, T, S: SieveFactory<T>> Iterator for SieveIterator<'a, R, T, S> {
-    type Item = T;
+impl<'a, R: CryptoRngCore, S: SieveFactory> Iterator for SieveIterator<'a, R, S> {
+    type Item = S::Item;
 
     fn next(&mut self) -> Option<Self::Item> {
         loop {
@@ -113,7 +117,8 @@ mod tests {
             count: usize,
         }
 
-        impl SieveFactory<usize> for TestSieveFactory {
+        impl SieveFactory for TestSieveFactory {
+            type Item = usize;
             type Sieve = core::ops::Range<usize>;
 
             fn make_sieve(
diff --git a/src/hazmat/sieve.rs b/src/hazmat/sieve.rs
index a3484aa..bceb0c9 100644
--- a/src/hazmat/sieve.rs
+++ b/src/hazmat/sieve.rs
@@ -2,6 +2,7 @@
 //! before proceeding with slower tests.
 
 use alloc::{vec, vec::Vec};
+use core::marker::PhantomData;
 use core::num::{NonZero, NonZeroU32};
 
 use crypto_bigint::{Integer, Odd, RandomBits};
@@ -247,12 +248,13 @@ impl<T: Integer> Iterator for SmallPrimesSieve<T> {
 
 /// A sieve returning numbers that are not multiples of a set of small factors.
 #[derive(Debug, Clone, Copy)]
-pub struct SmallPrimesSieveFactory {
+pub struct SmallPrimesSieveFactory<T> {
     max_bit_length: NonZeroU32,
     safe_primes: bool,
+    phantom: PhantomData<T>,
 }
 
-impl SmallPrimesSieveFactory {
+impl<T: Integer + RandomBits> SmallPrimesSieveFactory<T> {
     fn new_impl(max_bit_length: u32, safe_primes: bool) -> Self {
         if !safe_primes && max_bit_length < 2 {
             panic!("`bit_length` must be 2 or greater.");
@@ -264,6 +266,7 @@ impl SmallPrimesSieveFactory {
         Self {
             max_bit_length,
             safe_primes,
+            phantom: PhantomData,
         }
     }
 
@@ -280,7 +283,8 @@ impl SmallPrimesSieveFactory {
     }
 }
 
-impl<T: Integer + RandomBits> SieveFactory<T> for SmallPrimesSieveFactory {
+impl<T: Integer + RandomBits> SieveFactory for SmallPrimesSieveFactory<T> {
+    type Item = T;
     type Sieve = SmallPrimesSieve<T>;
     fn make_sieve(
         &mut self,
@@ -446,12 +450,12 @@ mod tests {
     #[test]
     #[should_panic(expected = "`bit_length` must be 2 or greater")]
     fn too_few_bits_regular_primes() {
-        let _fac = SmallPrimesSieveFactory::new(1);
+        let _fac = SmallPrimesSieveFactory::<U64>::new(1);
     }
 
     #[test]
     #[should_panic(expected = "`bit_length` must be 3 or greater")]
     fn too_few_bits_safe_primes() {
-        let _fac = SmallPrimesSieveFactory::new_safe_primes(2);
+        let _fac = SmallPrimesSieveFactory::<U64>::new_safe_primes(2);
     }
 }
diff --git a/src/traits.rs b/src/traits.rs
index bf0e02f..53ef7fd 100644
--- a/src/traits.rs
+++ b/src/traits.rs
@@ -4,9 +4,12 @@ use rand_core::CryptoRngCore;
 use crate::{generate_prime_with_rng, generate_safe_prime_with_rng, is_prime_with_rng, is_safe_prime_with_rng};
 
 /// A type producing sieves for random prime generation.
-pub trait SieveFactory<T> {
+pub trait SieveFactory {
+    /// The type of items returning by the sieves.
+    type Item;
+
     /// The resulting sieve.
-    type Sieve: Iterator<Item = T>;
+    type Sieve: Iterator<Item = Self::Item>;
 
     /// Makes a sieve given an RNG and the previous exhausted sieve (if any).
     ///