diff --git a/CMakeLists.txt b/CMakeLists.txt
index e3af3bf6..11f3a055 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -48,6 +48,7 @@
 
 cmake_minimum_required(VERSION 3.13...3.16 FATAL_ERROR)
 
+include(CMakePushCheckState)
 include(CheckSymbolExists)
 include(CheckStructHasMember)
 include(cmake/tuklib_integer.cmake)
@@ -387,6 +388,20 @@ if(NOT TUKLIB_CPUCORES_FOUND OR NOT TUKLIB_PHYSMEM_FOUND)
             "To build anyway, edit this CMakeLists.txt to ignore this error.")
 endif()
 
+# Check for __attribute__((__constructor__)) support.
+# This needs -Werror because some compilers just warn
+# about this being unsupported.
+cmake_push_check_state()
+set(CMAKE_REQUIRED_FLAGS "-Werror")
+check_c_source_compiles("
+        __attribute__((__constructor__))
+        static void my_constructor_func(void) { return; }
+        int main(void) { return 0; }
+    "
+    HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR)
+cmake_pop_check_state()
+tuklib_add_definition_if(liblzma HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR)
+
 # immintrin.h:
 include(CheckIncludeFile)
 check_include_file(immintrin.h HAVE_IMMINTRIN_H)
diff --git a/INSTALL b/INSTALL
index a6c0551f..2c94ecea 100644
--- a/INSTALL
+++ b/INSTALL
@@ -456,7 +456,9 @@ XZ Utils Installation
 
                         no      Disable threading support. This is the
                                 same as using --disable-threads.
-                                NOTE: If combined with --enable-small, the
+                                NOTE: If combined with --enable-small
+                                and the compiler doesn't support
+                                __attribute__((__constructor__)), the
                                 resulting liblzma won't be thread safe,
                                 that is, if a multi-threaded application
                                 calls any liblzma functions from more than
diff --git a/configure.ac b/configure.ac
index 15b4ba4c..cf226b29 100644
--- a/configure.ac
+++ b/configure.ac
@@ -768,6 +768,29 @@ AC_CHECK_MEMBERS([
 AC_SYS_LARGEFILE
 AC_C_BIGENDIAN
 
+# __attribute__((__constructor__)) can be used for one-time initializations.
+# Use -Werror because some compilers accept unknown attributes and just
+# give a warning. If it works this should give no warnings, even
+# clang -Weverything should be fine.
+# dnl This doesn't need AC_LANG_SOURCE, minimal code is enough.
+AC_MSG_CHECKING([if __attribute__((__constructor__)) can be used])
+have_func_attribute_constructor=no
+OLD_CFLAGS="$CFLAGS"
+CFLAGS="$CFLAGS -Werror"
+AC_COMPILE_IFELSE([
+	__attribute__((__constructor__))
+	static void my_constructor_func(void) { return; }
+], [
+	AC_DEFINE([HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR], [1],
+		[Define to 1 if __attribute__((__constructor__))
+		is supported for functions.])
+	have_func_attribute_constructor=yes
+	AC_MSG_RESULT([yes])
+], [
+	AC_MSG_RESULT([no])
+])
+CFLAGS="$OLD_CFLAGS"
+
 
 ###############################################################################
 # Checks for library functions.
@@ -1005,9 +1028,11 @@ if test x$tuklib_cv_cpucores_method = xunknown; then
 	echo "No supported method to detect the number of CPU cores."
 fi
 
-if test "x$enable_threads$enable_small" = xnoyes; then
+if test "x$enable_threads$enable_small$have_func_attribute_constructor" \
+		= xnoyesno; then
 	echo
 	echo "NOTE:"
-	echo "liblzma will be thread unsafe due the combination"
-	echo "of --disable-threads --enable-small."
+	echo "liblzma will be thread-unsafe due to the combination"
+	echo "of --disable-threads --enable-small when using a compiler"
+	echo "that doesn't support __attribute__((__constructor__))."
 fi
diff --git a/src/liblzma/check/crc32_small.c b/src/liblzma/check/crc32_small.c
index 5f8a3286..186966e9 100644
--- a/src/liblzma/check/crc32_small.c
+++ b/src/liblzma/check/crc32_small.c
@@ -16,6 +16,9 @@
 uint32_t lzma_crc32_table[1][256];
 
 
+#ifdef HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR
+__attribute__((__constructor__))
+#endif
 static void
 crc32_init(void)
 {
@@ -37,18 +40,22 @@ crc32_init(void)
 }
 
 
+#ifndef HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR
 extern void
 lzma_crc32_init(void)
 {
 	mythread_once(crc32_init);
 	return;
 }
+#endif
 
 
 extern LZMA_API(uint32_t)
 lzma_crc32(const uint8_t *buf, size_t size, uint32_t crc)
 {
+#ifndef HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR
 	lzma_crc32_init();
+#endif
 
 	crc = ~crc;
 
diff --git a/src/liblzma/check/crc64_small.c b/src/liblzma/check/crc64_small.c
index 55d72316..420f7cfb 100644
--- a/src/liblzma/check/crc64_small.c
+++ b/src/liblzma/check/crc64_small.c
@@ -16,6 +16,9 @@
 static uint64_t crc64_table[256];
 
 
+#ifdef HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR
+__attribute__((__constructor__))
+#endif
 static void
 crc64_init(void)
 {
@@ -40,7 +43,9 @@ crc64_init(void)
 extern LZMA_API(uint64_t)
 lzma_crc64(const uint8_t *buf, size_t size, uint64_t crc)
 {
+#ifndef HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR
 	mythread_once(crc64_init);
+#endif
 
 	crc = ~crc;
 
diff --git a/src/liblzma/lz/lz_encoder.c b/src/liblzma/lz/lz_encoder.c
index 890d1bc4..2dad7e5f 100644
--- a/src/liblzma/lz/lz_encoder.c
+++ b/src/liblzma/lz/lz_encoder.c
@@ -543,7 +543,7 @@ lzma_lz_encoder_init(lzma_next_coder *next, const lzma_allocator *allocator,
 			const lzma_allocator *allocator, const void *options,
 			lzma_lz_options *lz_options))
 {
-#ifdef HAVE_SMALL
+#if defined(HAVE_SMALL) && !defined(HAVE_FUNC_ATTRIBUTE_CONSTRUCTOR)
 	// We need that the CRC32 table has been initialized.
 	lzma_crc32_init();
 #endif