diff --git a/pyproject.toml b/pyproject.toml
index e7c5be907..1ba68554d 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -22,11 +22,11 @@ dependencies = [
   # Some of these schema dependencies are minimums because we generated asdf
   # files with them unpinned so they are now required to read generated asdf
   # files.
-  "asdf>=2.14.4",
-  "asdf-astropy>=0.6.0",
-  "asdf-coordinates-schemas>=0.3.0",
-  "asdf-standard>=1.1.0",
-  "asdf-transform-schemas>=0.5.0",
+  "asdf>=2.11.2",
+  "asdf-astropy>=0.2.0",
+  "asdf-coordinates-schemas>=0.1.0",
+  "asdf-standard>=1.0.3",
+  "asdf-transform-schemas>=0.3.0",
   "asdf-wcs-schemas>=0.3.0",
   "astropy>=5.3",
   "dask[array]>=2021.8.0",
diff --git a/tox.ini b/tox.ini
index 282c91f2e..f69177db0 100644
--- a/tox.ini
+++ b/tox.ini
@@ -60,8 +60,11 @@ commands =
     # !online: {env:PYTEST_COMMAND} {posargs}
     # Then specify a specific one like this
     # online: {env:PYTEST_COMMAND} --remote-data=any {posargs}
-    !online: {env:PYTEST_COMMAND} {posargs}
-    online: {env:PYTEST_COMMAND} --remote-data=any {posargs}
+    {env:PYTEST_COMMAND} \
+    online: --remote-data=any \
+    # It's not possible to test the new schemas with the oldest dependencies
+    # as the new schemas require new dependent schemas
+    oldestdeps: -o asdf_schema_tests_enabled=false
 
 [testenv:codestyle]
 pypi_filter =