diff --git a/google/cloud/internal/openssl/ssl_ec_curves.cc b/google/cloud/internal/openssl/ssl_ec_curves.cc
index 5ffcd6a50c694..de2220a067b1d 100644
--- a/google/cloud/internal/openssl/ssl_ec_curves.cc
+++ b/google/cloud/internal/openssl/ssl_ec_curves.cc
@@ -17,7 +17,6 @@
 #include <openssl/ec.h>
 #include <openssl/ssl.h>
 #include <algorithm>
-#include <array>
 #include <memory>
 #include <string>
 #include <vector>
@@ -27,14 +26,12 @@ namespace cloud {
 namespace rest_internal {
 GOOGLE_CLOUD_CPP_INLINE_NAMESPACE_BEGIN
 
-#if OPENSSL_VERSION_NUMBER >= 0x30500000L || defined(OPENSSL_IS_BORINGSSL)
+#if OPENSSL_VERSION_NUMBER >= 0x30500000L
 namespace {
 struct OpenSslDeleter {
-#if OPENSSL_VERSION_NUMBER >= 0x30500000L
   void operator()(STACK_OF(OPENSSL_CSTRING) * ptr) {
     sk_OPENSSL_CSTRING_free(ptr);
   }
-#endif
   void operator()(SSL_CTX* ptr) { SSL_CTX_free(ptr); }
 };
 }  // namespace
@@ -56,44 +53,27 @@ std::vector<std::string> AvailableCryptoGroups() {
       if (name != nullptr) groups.emplace_back(name);
     }
   }
-#else  // OPENSSL_VERSION_NUMBER < 0x30500000L
-  std::vector<std::string> builtin_groups;
+#elif defined(OPENSSL_IS_BORINGSSL) && defined(SSL_GROUP_SECP256R1)
+  // BoringSSL reports the names of all the TLS groups it supports. It added
+  // `SSL_get_all_group_names()` in the same change as the `SSL_GROUP_*`
+  // macros, so we use the latter to detect the former.
+  std::vector<char const*> names(SSL_get_all_group_names(nullptr, 0));
+  SSL_get_all_group_names(names.data(), names.size());
+  for (char const* name : names) {
+    if (name != nullptr) groups.emplace_back(name);
+  }
+#elif defined(OPENSSL_IS_BORINGSSL)
+  // Versions of BoringSSL without `SSL_get_all_group_names()` predate support
+  // for X25519MLKEM768. Returning an empty list leaves the library's default
+  // groups unchanged.
+#else   // OpenSSL < 3.5
   size_t const num_curves = EC_get_builtin_curves(nullptr, 0);
   std::vector<EC_builtin_curve> builtin(num_curves);
   EC_get_builtin_curves(builtin.data(), num_curves);
   for (auto const& c : builtin) {
     char const* name = OBJ_nid2sn(c.nid);
-    if (name != nullptr) builtin_groups.emplace_back(name);
-  }
-#ifdef OPENSSL_IS_BORINGSSL
-  // "secp224r1" can be included in the builtin curves, but it results in a
-  // "CURL error [59]=Couldn't use specified SSL cipher" error.
-  for (auto const& curve : builtin_groups) {
-    if (curve == "secp224r1") continue;
-    groups.emplace_back(curve);
-  }
-
-  // Unlike OpenSSL, BoringSSL does not provide a way to query the available
-  // curves, so we have to probe the library using a temporary SSL_CTX.
-  std::array<std::string_view, 3> constexpr kCandidates{
-      "X25519",
-      "X25519MLKEM768",
-      "X25519Kyber768Draft00",
-  };
-
-  auto ctx =
-      std::unique_ptr<SSL_CTX, OpenSslDeleter>(SSL_CTX_new(TLS_method()));
-  if (!ctx) return groups;
-  for (auto const& curve : kCandidates) {
-    // SSL_CTX_set1_curves_list returns 1 if the curve(s) are
-    // recognized/supported
-    if (SSL_CTX_set1_curves_list(ctx.get(), curve.data()) == 1) {
-      groups.emplace_back(curve);
-    }
+    if (name != nullptr) groups.emplace_back(name);
   }
-#else
-  groups = std::move(builtin_groups);
-#endif  // OPENSSL_IS_BORINGSSL
 #endif  // OPENSSL_VERSION_NUMBER >= 0x30500000L
   return groups;
 }