diff --git a/src/_native/helpers.cpp b/src/_native/helpers.cpp
index b81bfc9..4d59aa4 100644
--- a/src/_native/helpers.cpp
+++ b/src/_native/helpers.cpp
@@ -51,6 +51,15 @@ void err_SetFromWindowsErrWithMessage(int error, const char *message, const wcha
         cause = PyErr_GetRaisedException();
     }
 
+    if ((error & 0xFFFF0000) == 0x80070000) {
+        // Error code is an HRESULT containing a regular Windows error
+        error &= 0xFFFF;
+    }
+    if (!hModule && error >= 12000 && error <= 12184) {
+        // Error codes are from WinHTTP, which means we need a module
+        hModule = GetModuleHandleW(L"winhttp");
+    }
+
     if (!os_message) {
         DWORD len = FormatMessageW(
             /* Error API error */
diff --git a/tests/conftest.py b/tests/conftest.py
index d475ad5..6d99e0b 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -17,6 +17,8 @@
         if k[:1] not in ("", "_"):
             setattr(_native, k, getattr(_native_test, k))
 
+_native.coinitialize()
+
 
 # Importing in order carefully to ensure the variables we override are handled
 # correctly by submodules.
diff --git a/tests/test_shortcut.py b/tests/test_shortcut.py
index a965160..1243ff7 100644
--- a/tests/test_shortcut.py
+++ b/tests/test_shortcut.py
@@ -7,7 +7,6 @@
 
 def test_simple_shortcut(tmp_path):
     open(tmp_path / "target.txt", "wb").close()
-    _native.coinitialize()
     _native.shortcut_create(
         tmp_path / "test.lnk",
         tmp_path / "target.txt",
@@ -17,7 +16,6 @@ def test_simple_shortcut(tmp_path):
 
 
 def test_start_path():
-    _native.coinitialize()
     p = Path(_native.shortcut_get_start_programs())
     assert p.is_dir()
 
diff --git a/tests/test_urlutils.py b/tests/test_urlutils.py
index 14e5986..e78769e 100644
--- a/tests/test_urlutils.py
+++ b/tests/test_urlutils.py
@@ -227,7 +227,7 @@ def inject_error():
 def test_bits_errors(localserver, tmp_path, inject_error):
     import uuid
 
-    ERROR_MR_MID_NOT_FOUND = 0x8007013D
+    ERROR_MR_MID_NOT_FOUND = 0x13D
 
     dest = tmp_path / "read.txt"
     url = localserver + "/128kb"