diff --git a/setup.py b/setup.py
index 345d1ea752..4aa07904f7 100644
--- a/setup.py
+++ b/setup.py
@@ -32,11 +32,12 @@
 # 'Development Status :: 5 - Production/Stable'
 release_status = "Development Status :: 3 - Alpha"
 dependencies = [
+    # please keep these in sync with the minimum versions in testing/constraints-3.9.txt
     "cloudpickle >= 2.0.0",
     "fsspec >=2023.3.0",
     "gcsfs >=2023.3.0",
     "geopandas >=0.12.2",
-    "google-auth >2.14.1,<3.0dev",
+    "google-auth >=2.15.0,<3.0dev",
     "google-cloud-bigquery[bqstorage,pandas] >=3.10.0",
     "google-cloud-functions >=1.10.1",
     "google-cloud-bigquery-connection >=1.12.0",
@@ -51,6 +52,10 @@
     "requests >=2.27.1",
     "scikit-learn >=1.2.2",
     "sqlalchemy >=1.4,<3.0dev",
+    # Keep sqlglot versions in sync with ibis-framework. This avoids problems
+    # where the incorrect version of sqlglot is installed, such as
+    # https://github.com/googleapis/python-bigquery-dataframes/issues/315
+    "sqlglot >=19.9.0,<20",
     "tabulate >= 0.9",
     "ipywidgets >=7.7.1",
     "humanize >= 4.6.0",
diff --git a/testing/constraints-3.9.txt b/testing/constraints-3.9.txt
index 218255c77e..42cc68eb04 100644
--- a/testing/constraints-3.9.txt
+++ b/testing/constraints-3.9.txt
@@ -1,121 +1,24 @@
-argcomplete==2.1.2
-asyncmock==0.4.2
-atpublic==3.1.1
-attrs==22.2.0
-bidict==0.22.1
-black==23.3.0
-bleach==6.0.0
-cachetools==5.3.0
-certifi==2022.12.7
-cffi==1.15.1
-cfgv==3.3.1
-charset-normalizer==2.0.0
-click==8.1.3
+# please keep these in sync with the minimum versions in setup.py
 cloudpickle==2.0.0
-colorlog==6.7.0
-coverage==7.2.2
-cryptography==40.0.1
-distlib==0.3.6
-docstring-inheritance==2.0.0
-docutils==0.19
-exceptiongroup==1.1.1
-execnet==1.9.0
-filelock==3.10.7
 fsspec==2023.3.0
-gcp-docuploader==0.6.5
-gcp-releasetool==1.11.0
 gcsfs==2023.3.0
 geopandas==0.12.2
-google-api-core==2.11.0
-google-auth==2.17.0
-google-auth-oauthlib==1.0.0
+google-auth==2.15.0
 google-cloud-bigquery==3.10.0
-google-cloud-bigquery-connection==1.12.0
-google-cloud-bigquery-storage==2.19.1
-google-cloud-core==2.3.2
 google-cloud-functions==1.10.1
+google-cloud-bigquery-connection==1.12.0
 google-cloud-iam==2.12.1
 google-cloud-resource-manager==1.10.3
 google-cloud-storage==2.0.0
-google-cloud-testutils==1.3.3
-google-crc32c==1.5.0
-google-resumable-media==2.4.1
-googleapis-common-protos==1.59.0
-greenlet==2.0.2
-grpc-google-iam-v1==0.12.6
-grpcio==1.53.0
-grpcio-status==1.48.2
 ibis-framework==7.1.0
-humanize==4.6.0
-identify==2.5.22
-idna==3.4
-importlib-metadata==6.1.0
-iniconfig==2.0.0
-ipywidgets==7.7.1
-jaraco.classes==3.2.3
-jeepney==0.8.0
-Jinja2==3.1.2
-keyring==23.13.1
-markdown-it-py==2.2.0
-MarkupSafe==2.1.2
-mdurl==0.1.2
-mock==5.0.1
-more-itertools==9.1.0
-multipledispatch==0.6.0
-mypy-extensions==1.0.0
-nodeenv==1.7.0
-nox==2022.11.21
-numpy==1.24.2
-oauthlib==3.2.2
-packaging==23.0
 pandas==1.5.0
-pandas-gbq==0.19.0
-parsy==2.1
-pathspec==0.11.1
-pkginfo==1.9.6
-platformdirs==3.2.0
-pluggy==1.0.0
-pooch==1.7.0
-pre-commit==3.2.1
-proto-plus==1.22.2
-protobuf==3.20.3
-pyarrow==11.0.0
-pyasn1==0.4.8
-pyasn1-modules==0.2.8
-pycparser==2.21
 pydata-google-auth==1.8.2
-Pygments==2.14.0
-PyJWT==2.6.0
-pyperclip==1.8.2
-pytest==7.2.2
-pytest-asyncio==0.21.0
-pytest-cov==4.0.0
-pytest-mock==3.11.1
-pytest-retry==1.1.0
-pytest-xdist==3.2.1
-python-dateutil==2.8.2
-pytz==2023.3
-PyYAML==6.0
-readme-renderer==37.3
 requests==2.27.1
-requests-oauthlib==1.3.1
-requests-toolbelt==0.10.1
-rfc3986==2.0.0
-rich==13.3.3
-rsa==4.9
 scikit-learn==1.2.2
-SecretStorage==3.3.3
-six==1.16.0
-SQLAlchemy==1.4.0
-sqlglot==18.12.0
-tomli==2.0.1
-toolz==0.12.0
-tqdm==4.65.0
-twine==4.0.2
-typing_extensions==4.5.0
-tzdata==2023.3
-urllib3==1.26.15
-virtualenv==20.21.0
-webencodings==0.5.1
-xxhash==3.2.0
-zipp==3.15.0
+sqlalchemy==1.4
+sqlglot==19.9.0
+tabulate==0.9
+ipywidgets==7.7.1
+humanize==4.6.0
+# extras
+pandas-gbq==0.19.0