diff --git a/asdf/_tests/tags/core/tests/test_ndarray.py b/asdf/_tests/tags/core/tests/test_ndarray.py
index 5de7a0ce4..d0aac5d8a 100644
--- a/asdf/_tests/tags/core/tests/test_ndarray.py
+++ b/asdf/_tests/tags/core/tests/test_ndarray.py
@@ -167,12 +167,42 @@ def check_raw_yaml(content):
 
 
 def test_array_inline_threshold_recursive(tmpdir):
-    models = pytest.importorskip("astropy.modeling.models")
+    """
+    Test that setting the inline threshold works for objects
+    that contain (and when serialized produce a ndarray)
+    """
+
+    class NDArrayContainer:
+        def __init__(self, array):
+            self._array = array
+
+        @property
+        def array(self):
+            return np.array(self._array)
+
+
+    class NDArrayContainerConverter:
+        tags = ["http://somewhere.org/tags/foo-1.0.0"]
+        types = [NDArrayContainer]
+
+        def to_yaml_tree(self, obj, tag, ctx):
+            return {'array': obj.array}
+
+        def from_yaml_tree(self, node, tag, ctx):
+            return NDArrayContainer(node['array'])
+
+
+    class NDArrayContainerExtension:
+        tags = NDArrayContainerConverter.tags
+        converters = [NDArrayContainerConverter()]
+        extension_uri = "http://somewhere.org/extensions/foo-1.0.0"
+
 
-    aff = models.AffineTransformation2D(matrix=[[1, 2], [3, 4]])
-    tree = {"test": aff}
+    container = NDArrayContainer([[1, 2], [3, 4]])
+    tree = {"test": container}
 
     with asdf.config_context() as config:
+        config.add_extension(NDArrayContainerExtension())
         config.array_inline_threshold = 100
         # we can no longer use _helpers.assert_roundtrip_tree here because
         # the model no longer has a CustomType which results in equality testing
diff --git a/asdf/_tests/test_api.py b/asdf/_tests/test_api.py
index c8a49f8f9..bbf03009d 100644
--- a/asdf/_tests/test_api.py
+++ b/asdf/_tests/test_api.py
@@ -7,7 +7,6 @@
 
 import numpy as np
 import pytest
-from astropy.modeling import models
 from numpy.testing import assert_array_equal
 
 import asdf
@@ -119,23 +118,6 @@ def test_atomic_write(tmp_path, small_tree):
         ff.write_to(tmpfile)
 
 
-def test_overwrite(tmp_path):
-    """
-    This is intended to reproduce the following issue:
-    https://github.com/asdf-format/asdf/issues/100
-    """
-    tmpfile = str(tmp_path / "test.asdf")
-    aff = models.AffineTransformation2D(matrix=[[1, 2], [3, 4]])
-    f = asdf.AsdfFile()
-    f.tree["model"] = aff
-    f.write_to(tmpfile)
-    model = f.tree["model"]
-
-    ff = asdf.AsdfFile()
-    ff.tree["model"] = model
-    ff.write_to(tmpfile)
-
-
 def test_default_version():
     """
     See https://github.com/asdf-format/asdf/issues/364
diff --git a/asdf/_tests/test_file_format.py b/asdf/_tests/test_file_format.py
index 0f7b249ce..59b24e1ae 100644
--- a/asdf/_tests/test_file_format.py
+++ b/asdf/_tests/test_file_format.py
@@ -59,7 +59,6 @@ def test_no_final_newline(tmp_path):
         assert len(ff.tree) == 2
 
 
-@pytest.mark.filterwarnings("ignore::astropy.io.fits.verify.VerifyWarning")
 def test_no_asdf_header(tmp_path):
     content = b"What? This ain't no ASDF file"
 
@@ -157,7 +156,6 @@ def test_empty_file():
         assert len(ff._blocks) == 0
 
 
-@pytest.mark.filterwarnings("ignore::astropy.io.fits.verify.VerifyWarning")
 @pytest.mark.filterwarnings("ignore::asdf.exceptions.AsdfDeprecationWarning")
 def test_not_asdf_file():
     buff = io.BytesIO(b"SIMPLE")
diff --git a/asdf/_tests/test_schema.py b/asdf/_tests/test_schema.py
index 9d0f9e5f3..f868b82d0 100644
--- a/asdf/_tests/test_schema.py
+++ b/asdf/_tests/test_schema.py
@@ -37,22 +37,42 @@ def from_tree(cls, tree, ctx):
 
 
 def test_tagging_scalars():
-    pytest.importorskip("astropy", "3.0.0")
-    from astropy import units as u
+    class Scalar:
+        def __init__(self, value):
+            self.value = value
 
-    yaml = """
-unit: !unit/unit-1.0.0
+    scalar_tag = 'http://somewhere.org/tags/scalar-1.0.0'
+    class ScalarConverter:
+        tags = [scalar_tag]
+        types = [Scalar]
+
+        def to_yaml_tree(self, obj, tag, ctx):
+            return obj.value
+
+        def from_yaml_tree(self, node, tag, ctx):
+            return Scalar(node)
+
+    class ScalarExtension:
+        tags = [scalar_tag]
+        converters = [ScalarConverter()]
+        extension_uri = 'http://somewhere.org/extensions/scalar-1.0.0'
+
+    yaml = f"""
+tagged: !<{scalar_tag}>
   m
-not_unit:
+not_tagged:
   m
     """
-    buff = helpers.yaml_to_asdf(yaml)
-    with asdf.open(buff) as ff:
-        assert isinstance(ff.tree["unit"], u.UnitBase)
-        assert not isinstance(ff.tree["not_unit"], u.UnitBase)
-        assert isinstance(ff.tree["not_unit"], str)
+    with asdf.config_context() as cfg:
+        cfg.add_extension(ScalarExtension())
+        buff = helpers.yaml_to_asdf(yaml)
+        with asdf.open(buff) as ff:
+            assert isinstance(ff.tree["tagged"], Scalar)
+            assert not isinstance(ff.tree["not_tagged"], Scalar)
+            assert isinstance(ff.tree["not_tagged"], str)
 
-        assert ff.tree == {"unit": u.m, "not_unit": "m"}
+            assert ff.tree["tagged"].value == "m"
+            assert ff.tree["not_tagged"] == "m"
 
 
 def test_read_json_schema():
@@ -807,8 +827,6 @@ def test_nested_array_yaml(tmp_path):
 
 
 def test_type_missing_dependencies():
-    pytest.importorskip("astropy", "3.0.0")
-
     with pytest.warns(AsdfDeprecationWarning, match=".*subclasses the deprecated CustomType.*"):
 
         class MissingType(types.CustomType):
diff --git a/pyproject.toml b/pyproject.toml
index 64118a498..c992b2e57 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -44,7 +44,6 @@ docs = [
   'tomli; python_version < "3.11"',
 ]
 tests = [
-  "astropy>=5.0.4",
   "fsspec[http]>=2022.8.2",
   "lz4>=0.10",
   "psutil",