diff --git a/test/src/unit-udt.cpp b/test/src/unit-udt.cpp
index 12770ce64..bab9151af 100644
--- a/test/src/unit-udt.cpp
+++ b/test/src/unit-udt.cpp
@@ -38,6 +38,9 @@ using nlohmann::json;
 #include <memory>
 #include <utility>
 
+DOCTEST_GCC_SUPPRESS_WARNING_PUSH
+DOCTEST_GCC_SUPPRESS_WARNING("-Wnoexcept")
+
 namespace udt
 {
 enum class country
@@ -845,3 +848,5 @@ TEST_CASE("Issue #1237")
     struct non_convertible_type {};
     static_assert(!std::is_convertible<json, non_convertible_type>::value, "");
 }
+
+DOCTEST_GCC_SUPPRESS_WARNING_POP
diff --git a/test/src/unit-unicode2.cpp b/test/src/unit-unicode2.cpp
index 074704bba..d2effdcfe 100644
--- a/test/src/unit-unicode2.cpp
+++ b/test/src/unit-unicode2.cpp
@@ -41,6 +41,10 @@ using nlohmann::json;
 #include <iomanip>
 #include <test_data.hpp>
 
+// this test suite uses static variables with non-trivial destructors
+DOCTEST_CLANG_SUPPRESS_WARNING_PUSH
+DOCTEST_CLANG_SUPPRESS_WARNING("-Wexit-time-destructors")
+
 namespace
 {
 extern size_t calls;
@@ -623,3 +627,5 @@ TEST_CASE("Unicode (2/5)" * doctest::skip())
         }
     }
 }
+
+DOCTEST_CLANG_SUPPRESS_WARNING_POP