diff --git a/src/lib/pubkey/dilithium/dilithium_common/dilithium_algos.cpp b/src/lib/pubkey/dilithium/dilithium_common/dilithium_algos.cpp
index a0604a9cf6..8d4fd3f45e 100644
--- a/src/lib/pubkey/dilithium/dilithium_common/dilithium_algos.cpp
+++ b/src/lib/pubkey/dilithium/dilithium_common/dilithium_algos.cpp
@@ -523,24 +523,14 @@ DilithiumSerializedCommitment encode_commitment(const DilithiumPolyVec& w1, cons
  * NIST FIPS 204, Algorithm 29 (SampleInBall)
  */
 DilithiumPoly sample_in_ball(StrongSpan<const DilithiumCommitmentHash> seed, const DilithiumConstants& mode) {
-   auto xof = mode.symmetric_primitives().H(seed);
-
    // This generator resembles the while loop in the spec.
-   auto next_byte_lower_than = [&xof, n = uint16_t(0)](size_t i) mutable -> uint8_t {
-      while(n < DilithiumConstants::SAMPLE_IN_BALL_XOF_BOUND) {
-         ++n;
-         if(const uint8_t b = xof.output_next_byte(); b <= i) {
-            return b;
-         }
-      }
-
-      throw Internal_Error("SampleInBall did not terminate");
-   };
+   auto& xof = mode.symmetric_primitives().H(seed);
+   auto bounded_xof = Bounded_XOF<DilithiumConstants::SAMPLE_IN_BALL_XOF_BOUND + 8>(xof);
 
    DilithiumPoly c;
-   uint64_t signs = load_le(xof.output<8>());
+   uint64_t signs = load_le(bounded_xof.next<8>());
    for(size_t i = c.size() - mode.tau(); i < c.size(); ++i) {
-      const auto j = next_byte_lower_than(i);
+      const auto j = bounded_xof.next_byte([i](uint8_t byte) { return byte <= i; });
       c[i] = c[j];
       c[j] = 1 - 2 * (signs & 1);
       signs >>= 1;
@@ -565,25 +555,13 @@ void sample_ntt_uniform(StrongSpan<const DilithiumSeedRho> rho,
     * A generator that returns the next coefficient sampled from the XOF,
     * according to: NIST FIPS 204, Algorithm 14 (CoeffFromThreeBytes).
     */
-   auto next_coeff = [n = uint16_t(0)](Botan::XOF& xof) mutable -> uint32_t {
-      std::array<uint8_t, 4> bytes = {0};
-      std::span<uint8_t, 3> sampling_sink_in_bytes = std::span{bytes}.first<3>();
-
-      while(n < DilithiumConstants::SAMPLE_NTT_POLY_FROM_XOF_BOUND) {
-         n += static_cast<uint16_t>(sampling_sink_in_bytes.size());
-         xof.output(sampling_sink_in_bytes);
-         const auto z = load_le(bytes) & 0x7FFFFF;
-         if(z < DilithiumConstants::Q) {
-            return z;
-         }
-      }
-
-      throw Internal_Error("RejNTTPoly did not terminate");
-   };
-
    auto& xof = mode.symmetric_primitives().H(rho, nonce);
+   auto bounded_xof = Bounded_XOF<DilithiumConstants::SAMPLE_NTT_POLY_FROM_XOF_BOUND>(xof);
+
    for(auto& coeff : p) {
-      coeff = next_coeff(xof);
+      coeff =
+         bounded_xof.next<3>([](const auto bytes) { return make_uint32(0, bytes[2], bytes[1], bytes[0]) & 0x7FFFFF; },
+                             [](const uint32_t z) { return z < DilithiumConstants::Q; });
    }
 
    BOTAN_DEBUG_ASSERT(p.ct_validate_value_range(0, DilithiumConstants::Q - 1));
@@ -617,15 +595,15 @@ void sample_uniform_eta(DilithiumPoly& p, Botan::XOF& xof) {
    // A generator that returns the next coefficient sampled from the XOF. As the
    // sampling uses half-bytes, this keeps track of the additionally sampled
    // coefficient as needed.
-   auto next_coeff = [&xof, stashed_coeff = std::optional<int32_t>{}, n = uint16_t(0)]() mutable -> int32_t {
+   auto next_coeff = [bounded_xof = Bounded_XOF<DilithiumConstants::SAMPLE_POLY_FROM_XOF_BOUND>(xof),
+                      stashed_coeff = std::optional<int32_t>{}]() mutable -> int32_t {
       if(auto stashed = std::exchange(stashed_coeff, std::nullopt)) {
          return *stashed;
       }
 
       BOTAN_DEBUG_ASSERT(!stashed_coeff.has_value());
-      while(n < DilithiumConstants::SAMPLE_POLY_FROM_XOF_BOUND) {
-         ++n;
-         const auto b = xof.output_next_byte();
+      while(true) {
+         const auto b = bounded_xof.next_byte();
          const auto z0 = coeff_from_halfbyte<eta>(b & 0x0F);
          const auto z1 = coeff_from_halfbyte<eta>(b >> 4);
 
@@ -637,8 +615,6 @@ void sample_uniform_eta(DilithiumPoly& p, Botan::XOF& xof) {
             return *z1;
          }
       }
-
-      throw Internal_Error("RejBoundedPoly did not terminate");
    };
 
    for(auto& coeff : p) {