diff --git a/mypy/test/data.py b/mypy/test/data.py
index a04c87f60a8d..2bb727e27e71 100644
--- a/mypy/test/data.py
+++ b/mypy/test/data.py
@@ -18,7 +18,7 @@
 
 # File modify/create operation: copy module contents from source_path.
 UpdateFile = NamedTuple('UpdateFile', [('module', str),
-                                       ('source_path', str),
+                                       ('content', str),
                                        ('target_path', str)])
 
 # File delete operation: delete module file.
@@ -270,11 +270,35 @@ def setup(self) -> None:
         self.tmpdir = tempfile.TemporaryDirectory(prefix='mypy-test-')
         os.chdir(self.tmpdir.name)
         os.mkdir(test_temp_dir)
+
+        # Precalculate steps for find_steps()
+        steps: Dict[int, List[FileOperation]] = {}
+
         for path, content in self.files:
-            dir = os.path.dirname(path)
-            os.makedirs(dir, exist_ok=True)
-            with open(path, 'w', encoding='utf8') as f:
-                f.write(content)
+            m = re.match(r'.*\.([0-9]+)$', path)
+            if m:
+                # Skip writing subsequent incremental steps - rather
+                # store them as operations.
+                num = int(m.group(1))
+                assert num >= 2
+                target_path = re.sub(r'\.[0-9]+$', '', path)
+                module = module_from_path(target_path)
+                operation = UpdateFile(module, content, target_path)
+                steps.setdefault(num, []).append(operation)
+            else:
+                # Write the first incremental steps
+                dir = os.path.dirname(path)
+                os.makedirs(dir, exist_ok=True)
+                with open(path, 'w', encoding='utf8') as f:
+                    f.write(content)
+
+        for num, paths in self.deleted_paths.items():
+            assert num >= 2
+            for path in paths:
+                module = module_from_path(path)
+                steps.setdefault(num, []).append(DeleteFile(module, path))
+        max_step = max(steps) if steps else 2
+        self.steps = [steps.get(num, []) for num in range(2, max_step + 1)]
 
     def teardown(self) -> None:
         assert self.old_cwd is not None and self.tmpdir is not None, \
@@ -312,23 +336,7 @@ def find_steps(self) -> List[List[FileOperation]]:
 
         Defaults to having two steps if there aern't any operations.
         """
-        steps: Dict[int, List[FileOperation]] = {}
-        for path, _ in self.files:
-            m = re.match(r'.*\.([0-9]+)$', path)
-            if m:
-                num = int(m.group(1))
-                assert num >= 2
-                target_path = re.sub(r'\.[0-9]+$', '', path)
-                module = module_from_path(target_path)
-                operation = UpdateFile(module, path, target_path)
-                steps.setdefault(num, []).append(operation)
-        for num, paths in self.deleted_paths.items():
-            assert num >= 2
-            for path in paths:
-                module = module_from_path(path)
-                steps.setdefault(num, []).append(DeleteFile(module, path))
-        max_step = max(steps) if steps else 2
-        return [steps.get(num, []) for num in range(2, max_step + 1)]
+        return self.steps
 
 
 def module_from_path(path: str) -> str:
diff --git a/mypy/test/helpers.py b/mypy/test/helpers.py
index 2d7d5e59430c..fbd44bca868b 100644
--- a/mypy/test/helpers.py
+++ b/mypy/test/helpers.py
@@ -406,7 +406,7 @@ def split_lines(*streams: bytes) -> List[str]:
     ]
 
 
-def copy_and_fudge_mtime(source_path: str, target_path: str) -> None:
+def write_and_fudge_mtime(content: str, target_path: str) -> None:
     # In some systems, mtime has a resolution of 1 second which can
     # cause annoying-to-debug issues when a file has the same size
     # after a change. We manually set the mtime to circumvent this.
@@ -418,8 +418,10 @@ def copy_and_fudge_mtime(source_path: str, target_path: str) -> None:
     if os.path.isfile(target_path):
         new_time = os.stat(target_path).st_mtime + 1
 
-    # Use retries to work around potential flakiness on Windows (AppVeyor).
-    retry_on_error(lambda: shutil.copy(source_path, target_path))
+    dir = os.path.dirname(target_path)
+    os.makedirs(dir, exist_ok=True)
+    with open(target_path, "w", encoding="utf-8") as target:
+        target.write(content)
 
     if new_time:
         os.utime(target_path, times=(new_time, new_time))
@@ -430,7 +432,7 @@ def perform_file_operations(
     for op in operations:
         if isinstance(op, UpdateFile):
             # Modify/create file
-            copy_and_fudge_mtime(op.source_path, op.target_path)
+            write_and_fudge_mtime(op.content, op.target_path)
         else:
             # Delete file/directory
             if os.path.isdir(op.path):
diff --git a/test-data/unit/daemon.test b/test-data/unit/daemon.test
index 862ae57bc096..c73be05e1be3 100644
--- a/test-data/unit/daemon.test
+++ b/test-data/unit/daemon.test
@@ -274,7 +274,7 @@ bar.py:3: (str)
 bar.py:4: (arg=str)
 $ dmypy suggest foo.foo
 (str) -> int
-$ {python} -c "import shutil; shutil.copy('foo.py.2', 'foo.py')"
+$ {python} -c "import shutil; shutil.copy('foo2.py', 'foo.py')"
 $ dmypy check foo.py bar.py
 bar.py:3: error: Incompatible types in assignment (expression has type "int", variable has type "str")
 == Return code: 1
@@ -284,7 +284,7 @@ def foo(arg):
 class Bar:
     def bar(self): pass
 var = 0
-[file foo.py.2]
+[file foo2.py]
 def foo(arg: str) -> int:
     return 12
 class Bar:
diff --git a/test-data/unit/fine-grained-follow-imports.test b/test-data/unit/fine-grained-follow-imports.test
index 1bb62adbe552..67b99abaf93f 100644
--- a/test-data/unit/fine-grained-follow-imports.test
+++ b/test-data/unit/fine-grained-follow-imports.test
@@ -638,6 +638,7 @@ import p2.m2
 p1/m1.py:1: error: "int" not callable
 main.py:2: error: Cannot find implementation or library stub for module named "p2.m2"
 main.py:2: note: See https://mypy.readthedocs.io/en/stable/running_mypy.html#missing-imports
+main.py:2: error: Cannot find implementation or library stub for module named "p2"
 ==
 p2/m2.py:1: error: "str" not callable
 p1/m1.py:1: error: "int" not callable