diff --git a/.github/workflows/hypothesis.yaml b/.github/workflows/hypothesis.yaml
index 1029063ef4..0a320de00b 100644
--- a/.github/workflows/hypothesis.yaml
+++ b/.github/workflows/hypothesis.yaml
@@ -69,6 +69,12 @@ jobs:
         path: .hypothesis/
         key: cache-hypothesis-${{ runner.os }}-${{ github.run_id }}
 
+    - name: Upload coverage
+      uses: codecov/codecov-action@v5
+      with:
+        token: ${{ secrets.CODECOV_TOKEN }}
+        verbose: true # optional (default = false)
+
     - name: Generate and publish the report
       if: |
         failure()
diff --git a/changes/2804.feature.rst b/changes/2804.feature.rst
new file mode 100644
index 0000000000..5a707752a0
--- /dev/null
+++ b/changes/2804.feature.rst
@@ -0,0 +1 @@
+:py:class:`LocalStore` learned to ``delete_dir``. This makes array and group deletes more efficient.
diff --git a/pyproject.toml b/pyproject.toml
index 6fbcd1991e..ab285ff7ff 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -161,7 +161,7 @@ run = "run-coverage --no-cov"
 run-pytest = "run"
 run-verbose = "run-coverage --verbose"
 run-mypy = "mypy src"
-run-hypothesis = "pytest --hypothesis-profile ci tests/test_properties.py tests/test_store/test_stateful*"
+run-hypothesis = "run-coverage --hypothesis-profile ci --run-slow-hypothesis tests/test_properties.py tests/test_store/test_stateful*"
 list-env = "pip list"
 
 [tool.hatch.envs.doctest]
@@ -398,7 +398,8 @@ filterwarnings = [
     "ignore:.*is currently not part in the Zarr format 3 specification.*:UserWarning",
 ]
 markers = [
-    "gpu: mark a test as requiring CuPy and GPU"
+    "gpu: mark a test as requiring CuPy and GPU",
+    "slow_hypothesis: slow hypothesis tests",
 ]
 
 [tool.repo-review]
diff --git a/src/zarr/storage/_local.py b/src/zarr/storage/_local.py
index 1defea26b4..b20a601bed 100644
--- a/src/zarr/storage/_local.py
+++ b/src/zarr/storage/_local.py
@@ -208,6 +208,19 @@ async def delete(self, key: str) -> None:
         else:
             await asyncio.to_thread(path.unlink, True)  # Q: we may want to raise if path is missing
 
+    async def delete_dir(self, prefix: str) -> None:
+        # docstring inherited
+        self._check_writable()
+        path = self.root / prefix
+        if path.is_dir():
+            shutil.rmtree(path)
+        elif path.is_file():
+            raise ValueError(f"delete_dir was passed a {prefix=!r} that is a file")
+        else:
+            # Non-existent directory
+            # This path is tested by test_group:test_create_creates_parents for one
+            pass
+
     async def exists(self, key: str) -> bool:
         # docstring inherited
         path = self.root / key
diff --git a/src/zarr/testing/stateful.py b/src/zarr/testing/stateful.py
index 1a1ef0e3a3..3e8dbcdf04 100644
--- a/src/zarr/testing/stateful.py
+++ b/src/zarr/testing/stateful.py
@@ -68,6 +68,9 @@ def can_add(self, path: str) -> bool:
     # -------------------- store operations -----------------------
     @rule(name=node_names, data=st.data())
     def add_group(self, name: str, data: DataObject) -> None:
+        # Handle possible case-insensitive file systems (e.g. MacOS)
+        if isinstance(self.store, LocalStore):
+            name = name.lower()
         if self.all_groups:
             parent = data.draw(st.sampled_from(sorted(self.all_groups)), label="Group parent")
         else:
@@ -90,6 +93,9 @@ def add_array(
         name: str,
         array_and_chunks: tuple[np.ndarray[Any, Any], tuple[int, ...]],
     ) -> None:
+        # Handle possible case-insensitive file systems (e.g. MacOS)
+        if isinstance(self.store, LocalStore):
+            name = name.lower()
         array, chunks = array_and_chunks
         fill_value = data.draw(npst.from_dtype(array.dtype))
         if self.all_groups:
@@ -135,6 +141,7 @@ def add_array(
     #     self.model.rename(from_group, new_path)
     #     self.repo.store.rename(from_group, new_path)
 
+    @precondition(lambda self: self.store.supports_deletes)
     @precondition(lambda self: len(self.all_arrays) >= 1)
     @rule(data=st.data())
     def delete_array_using_del(self, data: DataObject) -> None:
@@ -149,6 +156,7 @@ def delete_array_using_del(self, data: DataObject) -> None:
             del group[array_name]
         self.all_arrays.remove(array_path)
 
+    @precondition(lambda self: self.store.supports_deletes)
     @precondition(lambda self: len(self.all_groups) >= 2)  # fixme don't delete root
     @rule(data=st.data())
     def delete_group_using_del(self, data: DataObject) -> None:
@@ -284,6 +292,10 @@ def supports_partial_writes(self) -> bool:
     def supports_writes(self) -> bool:
         return self.store.supports_writes
 
+    @property
+    def supports_deletes(self) -> bool:
+        return self.store.supports_deletes
+
 
 class ZarrStoreStateMachine(RuleBasedStateMachine):
     """ "
@@ -366,6 +378,7 @@ def get_partial_values(self, data: DataObject) -> None:
             model_vals_ls,
         )
 
+    @precondition(lambda self: self.store.supports_deletes)
     @precondition(lambda self: len(self.model.keys()) > 0)
     @rule(data=st.data())
     def delete(self, data: DataObject) -> None:
diff --git a/src/zarr/testing/strategies.py b/src/zarr/testing/strategies.py
index 81bb482b06..5722f3c99e 100644
--- a/src/zarr/testing/strategies.py
+++ b/src/zarr/testing/strategies.py
@@ -1,3 +1,4 @@
+import sys
 from typing import Any
 
 import hypothesis.extra.numpy as npst
@@ -209,7 +210,7 @@ def basic_indices(draw: st.DrawFn, *, shape: tuple[int], **kwargs: Any) -> Any:
 
 
 def key_ranges(
-    keys: SearchStrategy = node_names, max_size: int | None = None
+    keys: SearchStrategy = node_names, max_size: int = sys.maxsize
 ) -> SearchStrategy[list[int]]:
     """
     Function to generate key_ranges strategy for get_partial_values()
@@ -218,10 +219,14 @@ def key_ranges(
         [(key, (range_start, range_end)),
          (key, (range_start, range_end)),...]
     """
+
+    def make_request(start: int, length: int) -> RangeByteRequest:
+        return RangeByteRequest(start, end=min(start + length, max_size))
+
     byte_ranges = st.builds(
-        RangeByteRequest,
+        make_request,
         start=st.integers(min_value=0, max_value=max_size),
-        end=st.integers(min_value=0, max_value=max_size),
+        length=st.integers(min_value=0, max_value=max_size),
     )
     key_tuple = st.tuples(keys, byte_ranges)
     return st.lists(key_tuple, min_size=1, max_size=10)
diff --git a/tests/conftest.py b/tests/conftest.py
index e9cd2b8120..9be675cb20 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -147,6 +147,24 @@ def zarr_format(request: pytest.FixtureRequest) -> ZarrFormat:
     raise ValueError(msg)
 
 
+def pytest_addoption(parser: Any) -> None:
+    parser.addoption(
+        "--run-slow-hypothesis",
+        action="store_true",
+        default=False,
+        help="run slow hypothesis tests",
+    )
+
+
+def pytest_collection_modifyitems(config: Any, items: Any) -> None:
+    if config.getoption("--run-slow-hypothesis"):
+        return
+    skip_slow_hyp = pytest.mark.skip(reason="need --run-slow-hypothesis option to run")
+    for item in items:
+        if "slow_hypothesis" in item.keywords:
+            item.add_marker(skip_slow_hyp)
+
+
 settings.register_profile(
     "ci",
     max_examples=1000,
diff --git a/tests/test_store/test_stateful.py b/tests/test_store/test_stateful.py
index 637eea882d..63df814ac9 100644
--- a/tests/test_store/test_stateful.py
+++ b/tests/test_store/test_stateful.py
@@ -1,14 +1,15 @@
 # Stateful tests for arbitrary Zarr stores.
 import pytest
 from hypothesis.stateful import (
-    Settings,
     run_state_machine_as_test,
 )
 
 from zarr.abc.store import Store
-from zarr.storage import LocalStore, MemoryStore, ZipStore
+from zarr.storage import LocalStore, ZipStore
 from zarr.testing.stateful import ZarrHierarchyStateMachine, ZarrStoreStateMachine
 
+pytestmark = pytest.mark.slow_hypothesis
+
 
 def test_zarr_hierarchy(sync_store: Store):
     def mk_test_instance_sync() -> ZarrHierarchyStateMachine:
@@ -16,10 +17,8 @@ def mk_test_instance_sync() -> ZarrHierarchyStateMachine:
 
     if isinstance(sync_store, ZipStore):
         pytest.skip(reason="ZipStore does not support delete")
-    if isinstance(sync_store, MemoryStore):
-        run_state_machine_as_test(
-            mk_test_instance_sync, settings=Settings(report_multiple_bugs=False, max_examples=50)
-        )
+
+    run_state_machine_as_test(mk_test_instance_sync)
 
 
 def test_zarr_store(sync_store: Store) -> None:
@@ -28,11 +27,10 @@ def mk_test_instance_sync() -> None:
 
     if isinstance(sync_store, ZipStore):
         pytest.skip(reason="ZipStore does not support delete")
-    elif isinstance(sync_store, LocalStore):
-        pytest.skip(reason="This test has errors")
-    elif isinstance(sync_store, MemoryStore):
-        run_state_machine_as_test(mk_test_instance_sync, settings=Settings(max_examples=50))
-    else:
-        run_state_machine_as_test(
-            mk_test_instance_sync, settings=Settings(report_multiple_bugs=True)
-        )
+
+    if isinstance(sync_store, LocalStore):
+        # This test uses arbitrary keys, which are passed to `set` and `delete`.
+        # It assumes that `set` and `delete` are the only two operations that modify state.
+        # But LocalStore, directories can hang around even after a key is delete-d.
+        pytest.skip(reason="Test isn't suitable for LocalStore.")
+    run_state_machine_as_test(mk_test_instance_sync)