diff --git a/openssl.go b/openssl.go
index fb4b65b..23e4530 100644
--- a/openssl.go
+++ b/openssl.go
@@ -169,20 +169,23 @@ func SetFIPS(enabled bool) error {
 		} else {
 			provName = providerNameDefault
 		}
-		// Check if there is any provider that matches props.
-		if C.go_openssl_OSSL_PROVIDER_available(nil, provName) != 1 {
-			// If not, fallback to provName provider.
-			if C.go_openssl_OSSL_PROVIDER_load(nil, provName) == nil {
-				return newOpenSSLError("OSSL_PROVIDER_try_load")
-			}
-			// Make sure we now have a provider available.
-			if C.go_openssl_OSSL_PROVIDER_available(nil, provName) != 1 {
-				return fail("SetFIPS(" + strconv.FormatBool(enabled) + ") not supported")
-			}
-		}
+		// Try to load the provider, but don't fail if it's not loaded.
+		// The built-in provides might not be present in the system, e.g. because
+		// third-party providers are being used or because the system is not well-configured.
+		C.go_openssl_OSSL_PROVIDER_try_load(nil, provName, 1)
+		C.go_openssl_ERR_clear_error()
+
+		// Enable FIPS mode in the default properties.
 		if C.go_openssl_EVP_default_properties_enable_fips(nil, mode) != 1 {
-			return newOpenSSLError("openssl: EVP_default_properties_enable_fips")
+			return newOpenSSLError("EVP_default_properties_enable_fips")
 		}
+
+		// See FIPS() for the rationale behind this check.
+		md := C.go_openssl_EVP_MD_fetch(nil, algorithmSHA256, nil)
+		if md == nil {
+			return newOpenSSLError("openssl: EVP_MD_fetch")
+		}
+		C.go_openssl_EVP_MD_free(md)
 		return nil
 	default:
 		panic(errUnsupportedVersion())
diff --git a/shims.h b/shims.h
index a28ddde..9f95a83 100644
--- a/shims.h
+++ b/shims.h
@@ -174,6 +174,7 @@ typedef void* GO_SHA_CTX_PTR;
 // #endif
 #define FOR_ALL_OPENSSL_FUNCTIONS \
 DEFINEFUNC(void, ERR_error_string_n, (unsigned long e, char *buf, size_t len), (e, buf, len)) \
+DEFINEFUNC(void, ERR_clear_error, (void), ()) \
 DEFINEFUNC_LEGACY_1(unsigned long, ERR_get_error_line, (const char **file, int *line), (file, line)) \
 DEFINEFUNC_3_0(unsigned long, ERR_get_error_all, (const char **file, int *line, const char **func, const char **data, int *flags), (file, line, func, data, flags)) \
 DEFINEFUNC_RENAMED_1_1(const char *, OpenSSL_version, SSLeay_version, (int type), (type)) \
@@ -196,7 +197,7 @@ DEFINEFUNC_LEGACY_1(int, FIPS_mode_set, (int r), (r)) \
 DEFINEFUNC_3_0(int, EVP_default_properties_is_fips_enabled, (GO_OSSL_LIB_CTX_PTR libctx), (libctx)) \
 DEFINEFUNC_3_0(int, EVP_default_properties_enable_fips, (GO_OSSL_LIB_CTX_PTR libctx, int enable), (libctx, enable)) \
 DEFINEFUNC_3_0(int, OSSL_PROVIDER_available, (GO_OSSL_LIB_CTX_PTR libctx, const char *name), (libctx, name)) \
-DEFINEFUNC_3_0(GO_OSSL_PROVIDER_PTR, OSSL_PROVIDER_load, (GO_OSSL_LIB_CTX_PTR libctx, const char *name), (libctx, name)) \
+DEFINEFUNC_3_0(GO_OSSL_PROVIDER_PTR, OSSL_PROVIDER_try_load, (GO_OSSL_LIB_CTX_PTR libctx, const char *name, int retain_fallbacks), (libctx, name, retain_fallbacks)) \
 DEFINEFUNC_3_0(const char *, OSSL_PROVIDER_get0_name, (const GO_OSSL_PROVIDER_PTR prov), (prov)) \
 DEFINEFUNC_3_0(GO_EVP_MD_PTR, EVP_MD_fetch, (GO_OSSL_LIB_CTX_PTR ctx, const char *algorithm, const char *properties), (ctx, algorithm, properties)) \
 DEFINEFUNC_3_0(void, EVP_MD_free, (GO_EVP_MD_PTR md), (md)) \