diff --git a/ChangeLog.d/makefile-python-windows.txt b/ChangeLog.d/makefile-python-windows.txt
new file mode 100644
index 0000000..57ccc1a
--- /dev/null
+++ b/ChangeLog.d/makefile-python-windows.txt
@@ -0,0 +1,4 @@
+Bugfix
+   * The GNU makefiles invoke python3 in preference to python except on Windows.
+     The check was accidentally not performed when cross-compiling for Windows
+     on Linux. Fix this. Fixes #4774.
diff --git a/tests/Makefile b/tests/Makefile
index 59ed45a..6be6f33 100644
--- a/tests/Makefile
+++ b/tests/Makefile
@@ -49,11 +49,15 @@
 ifdef SHARED
 SHARED_SUFFIX=.$(DLEXT)
 endif
-PYTHON ?= python
 else
 DLEXT ?= so
 EXEXT=
 SHARED_SUFFIX=
+endif
+
+ifdef WINDOWS
+PYTHON ?= python
+else
 PYTHON ?= $(shell if type python3 >/dev/null 2>/dev/null; then echo python3; else echo python; fi)
 endif
 
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 5954004..58f9437 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -8186,7 +8186,7 @@
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
 requires_config_enabled MBEDTLS_SHA256_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
 run_test    "DTLS fragmenting: both (MTU=512)" \
@@ -8217,7 +8217,7 @@
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
 run_test    "DTLS fragmenting: proxy MTU: auto-reduction (not valgrind)" \
@@ -8241,7 +8241,7 @@
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
 run_test    "DTLS fragmenting: proxy MTU: auto-reduction (with valgrind)" \
@@ -8293,7 +8293,7 @@
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
 run_test    "DTLS fragmenting: proxy MTU, simple handshake (MTU=512)" \
@@ -8342,7 +8342,7 @@
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
 run_test    "DTLS fragmenting: proxy MTU, simple handshake, nbio (MTU=512)" \
@@ -8378,7 +8378,7 @@
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
 run_test    "DTLS fragmenting: proxy MTU, resumed handshake" \
@@ -8407,7 +8407,7 @@
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
 requires_config_enabled MBEDTLS_SHA256_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_SSL_RENEGOTIATION
 requires_config_enabled MBEDTLS_CHACHAPOLY_C
 run_test    "DTLS fragmenting: proxy MTU, ChachaPoly renego" \
@@ -8438,7 +8438,7 @@
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
 requires_config_enabled MBEDTLS_SHA256_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_SSL_RENEGOTIATION
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
@@ -8470,7 +8470,7 @@
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
 requires_config_enabled MBEDTLS_SHA256_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_SSL_RENEGOTIATION
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_CCM_C
@@ -8502,7 +8502,7 @@
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
 requires_config_enabled MBEDTLS_SHA256_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_SSL_RENEGOTIATION
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_CIPHER_MODE_CBC
@@ -8535,7 +8535,7 @@
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
 requires_config_enabled MBEDTLS_SHA256_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_SSL_RENEGOTIATION
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_CIPHER_MODE_CBC
@@ -8564,7 +8564,7 @@
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
 client_needs_more_time 2
@@ -8588,7 +8588,7 @@
 requires_config_enabled MBEDTLS_SSL_PROTO_DTLS
 requires_config_enabled MBEDTLS_RSA_C
 requires_config_enabled MBEDTLS_ECDSA_C
-requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA
+requires_config_enabled MBEDTLS_KEY_EXCHANGE_ECDHE_ECDSA_ENABLED
 requires_config_enabled MBEDTLS_AES_C
 requires_config_enabled MBEDTLS_GCM_C
 client_needs_more_time 2
diff --git a/tests/suites/test_suite_psa_crypto_storage_format.misc.data b/tests/suites/test_suite_psa_crypto_storage_format.misc.data
index 114c402..48e3804 100644
--- a/tests/suites/test_suite_psa_crypto_storage_format.misc.data
+++ b/tests/suites/test_suite_psa_crypto_storage_format.misc.data
@@ -3,11 +3,9 @@
 # debugging changes to the test code or to the test case generation.
 
 PSA storage read: AES-GCM+CTR
-#depends_on:PSA_WANT_KEY_TYPE_AES:PSA_WANT_ALG_GCM:PSA_WANT_ALG_CTR
-depends_on:MBEDTLS_AES_C:MBEDTLS_GCM_C:MBEDTLS_CTR_C
+depends_on:PSA_WANT_KEY_TYPE_AES:PSA_WANT_ALG_GCM:PSA_WANT_ALG_CTR
 key_storage_read:PSA_KEY_LIFETIME_PERSISTENT:PSA_KEY_TYPE_AES:128:PSA_KEY_USAGE_EXPORT | PSA_KEY_USAGE_ENCRYPT:PSA_ALG_GCM:PSA_ALG_CTR:"404142434445464748494a4b4c4d4e4f":"505341004b45590000000000010000000024800001010000000250050010c00410000000404142434445464748494a4b4c4d4e4f":1
 
 PSA storage save: AES-GCM+CTR
-#depends_on:PSA_WANT_KEY_TYPE_AES
-depends_on:MBEDTLS_AES_C
+depends_on:PSA_WANT_KEY_TYPE_AES
 key_storage_save:PSA_KEY_LIFETIME_PERSISTENT:PSA_KEY_TYPE_AES:128:PSA_KEY_USAGE_EXPORT | PSA_KEY_USAGE_ENCRYPT:PSA_ALG_GCM:PSA_ALG_CTR:"404142434445464748494a4b4c4d4e4f":"505341004b45590000000000010000000024800001010000000250050010c00410000000404142434445464748494a4b4c4d4e4f"