diff --git a/ci/deps/travis-37-cov.yaml b/ci/deps/travis-37-cov.yaml
index d031dc1cc062f..7d5104a58ce83 100644
--- a/ci/deps/travis-37-cov.yaml
+++ b/ci/deps/travis-37-cov.yaml
@@ -1,6 +1,5 @@
 name: pandas-dev
 channels:
-  - defaults
   - conda-forge
 dependencies:
   - python=3.7.*
@@ -15,7 +14,6 @@ dependencies:
   # pandas dependencies
   - beautifulsoup4
   - botocore>=1.11
-  - cython>=0.29.16
   - dask
   - fastparquet>=0.3.2
   - fsspec>=0.7.4
@@ -31,16 +29,18 @@ dependencies:
   - odfpy
   - openpyxl
   - pandas-gbq
+  - google-cloud-bigquery>=1.27.2 # GH 36436
   - psycopg2
   - pyarrow>=0.15.0
-  - pymysql
+  - pymysql=0.7.11
   - pytables
   - python-snappy
+  - python-dateutil
   - pytz
   - s3fs>=0.4.0
   - scikit-learn
   - scipy
-  - sqlalchemy
+  - sqlalchemy=1.3.0
   - statsmodels
   - xarray
   - xlrd
@@ -51,5 +51,4 @@ dependencies:
     - brotlipy
     - coverage
     - pandas-datareader
-    - python-dateutil
     - pyxlsb
diff --git a/ci/deps/travis-37-locale.yaml b/ci/deps/travis-37-locale.yaml
index 8a0b5b043ceca..cd6341e80be24 100644
--- a/ci/deps/travis-37-locale.yaml
+++ b/ci/deps/travis-37-locale.yaml
@@ -25,10 +25,10 @@ dependencies:
   - numexpr
   - numpy
   - openpyxl
-  - pandas-gbq=0.12.0
+  - pandas-gbq
+  - google-cloud-bigquery>=1.27.2 # GH 36436
   - pyarrow>=0.17
   - psycopg2=2.7
-  - pyarrow>=0.15.0 # GH #35813
   - pymysql=0.7.11
   - pytables
   - python-dateutil