diff --git a/req/include/req_common.hpp b/req/include/req_common.hpp
index aaead872..4bd9f7f6 100755
--- a/req/include/req_common.hpp
+++ b/req/include/req_common.hpp
@@ -31,6 +31,8 @@ namespace datasketches {
 namespace req_constants {
   /// minimum value of parameter K
   const uint16_t MIN_K = 4;
+  /// maximum value of parameter K
+  const uint16_t MAX_K = 1024;
   /// initial number of sections
   const uint8_t INIT_NUM_SECTIONS = 3;
   /// multiplier for nominal capacity
diff --git a/req/include/req_sketch.hpp b/req/include/req_sketch.hpp
index 52295bd2..2e2bc309 100755
--- a/req/include/req_sketch.hpp
+++ b/req/include/req_sketch.hpp
@@ -98,12 +98,14 @@ class req_sketch {
 
   /**
    * Constructor
-   * @param k Controls the size and error of the sketch. It must be even and in the range [4, 1024], inclusive.
+   * @param k Controls the size and error of the sketch. It must be no greater than 1024.
+   * Values below 4 are raised to 4, and odd values are rounded down to the nearest even value.
    * Value of 12 roughly corresponds to 1% relative error guarantee at 95% confidence.
    * @param hra if true, the default, the high ranks are prioritized for better
    * accuracy. Otherwise the low ranks are prioritized for better accuracy.
    * @param comparator strict weak ordering function (see C++ named requirements: Compare)
    * @param allocator used by this sketch to allocate memory
+   * @throws std::invalid_argument if k is greater than 1024
    */
   explicit req_sketch(uint16_t k, bool hra = true, const Comparator& comparator = Comparator(),
       const Allocator& allocator = Allocator());
diff --git a/req/include/req_sketch_impl.hpp b/req/include/req_sketch_impl.hpp
index 7f0b4557..8acea8bc 100755
--- a/req/include/req_sketch_impl.hpp
+++ b/req/include/req_sketch_impl.hpp
@@ -30,7 +30,7 @@ template<typename T, typename C, typename A>
 req_sketch<T, C, A>::req_sketch(uint16_t k, bool hra, const C& comparator, const A& allocator):
 comparator_(comparator),
 allocator_(allocator),
-k_(std::max<uint8_t>(static_cast<int>(k) & -2, static_cast<int>(req_constants::MIN_K))), //rounds down one if odd
+k_(std::max<uint16_t>(static_cast<int>(k) & -2, static_cast<int>(req_constants::MIN_K))), //rounds down one if odd
 hra_(hra),
 max_nom_size_(0),
 num_retained_(0),
@@ -40,6 +40,9 @@ min_item_(),
 max_item_(),
 sorted_view_(nullptr)
 {
+  if (k > req_constants::MAX_K) {
+    throw std::invalid_argument("K must be <= " + std::to_string(req_constants::MAX_K) + ": " + std::to_string(k));
+  }
   grow();
 }
 
diff --git a/req/test/req_sketch_test.cpp b/req/test/req_sketch_test.cpp
index 8de8f865..c8cf5cbe 100755
--- a/req/test/req_sketch_test.cpp
+++ b/req/test/req_sketch_test.cpp
@@ -54,6 +54,39 @@ TEST_CASE("req sketch: empty", "[req_sketch]") {
   REQUIRE_THROWS_AS(sketch.get_PMF(split_points, 1), std::runtime_error);
 }
 
+TEST_CASE("req sketch: k above 255", "[req_sketch]") {
+  // k used to be truncated to 8 bits: 256 became 4 and 500 became 244
+  REQUIRE(req_sketch<float>(256).get_k() == 256);
+  REQUIRE(req_sketch<float>(500).get_k() == 500);
+  REQUIRE(req_sketch<float>(1024).get_k() == 1024);
+  REQUIRE(req_sketch<float>(1001).get_k() == 1000); // rounds down if odd
+
+  req_sketch<float> sketch(1024);
+  const size_t n = 100000;
+  for (size_t i = 0; i < n; i++) sketch.update(static_cast<float>(i));
+  REQUIRE(sketch.is_estimation_mode());
+  auto bytes = sketch.serialize();
+  auto sketch2 = req_sketch<float>::deserialize(bytes.data(), bytes.size());
+  REQUIRE(sketch2.get_k() == 1024);
+  REQUIRE(sketch2.get_n() == n);
+  REQUIRE(sketch2.get_num_retained() == sketch.get_num_retained());
+}
+
+TEST_CASE("req sketch: k bounds", "[req_sketch]") {
+  for (bool hra: {true, false}) {
+    REQUIRE(req_sketch<float>(0, hra).get_k() == 4);
+    REQUIRE(req_sketch<float>(3, hra).get_k() == 4);
+    REQUIRE(req_sketch<float>(4, hra).get_k() == 4);
+    REQUIRE(req_sketch<float>(5, hra).get_k() == 4);
+    REQUIRE(req_sketch<float>(1023, hra).get_k() == 1022);
+    REQUIRE(req_sketch<float>(1024, hra).get_k() == 1024);
+    // Reject the original k, even if rounding down would put it in range.
+    REQUIRE_THROWS_AS(req_sketch<float>(1025, hra), std::invalid_argument);
+    REQUIRE_THROWS_AS(req_sketch<float>(1026, hra), std::invalid_argument);
+    REQUIRE_THROWS_AS(req_sketch<float>(std::numeric_limits<uint16_t>::max(), hra), std::invalid_argument);
+  }
+}
+
 TEST_CASE("req sketch: single value, lra", "[req_sketch]") {
   req_sketch<float> sketch(12, false);
   sketch.update(1.0f);