diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 409b1ac8c9df3..1e4e43ac03815 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -1,28 +1,20 @@
 # Adapted from https://github.com/numba/numba/blob/master/azure-pipelines.yml
 jobs:
-# Mac and Linux could potentially use the same template
-# except it isn't clear how to use a different build matrix
-# for each, so for now they are separate
-- template: ci/azure/macos.yml
+# Mac and Linux use the same template
+- template: ci/azure/posix.yml
   parameters:
     name: macOS
     vmImage: xcode9-macos10.13
-- template: ci/azure/linux.yml
+- template: ci/azure/posix.yml
   parameters:
     name: Linux
     vmImage: ubuntu-16.04
 
-# Windows Python 2.7 needs VC 9.0 installed, and not sure
-# how to make that a conditional task, so for now these are
-# separate templates as well
+# Windows Python 2.7 needs VC 9.0 installed, handled in the template
 - template: ci/azure/windows.yml
   parameters:
     name: Windows
     vmImage: vs2017-win2016
-- template: ci/azure/windows-py27.yml
-  parameters:
-    name: WindowsPy27
-    vmImage: vs2017-win2016
 
 - job: 'Checks_and_doc'
   pool:
diff --git a/ci/azure/linux.yml b/ci/azure/linux.yml
deleted file mode 100644
index fe64307e9d08f..0000000000000
--- a/ci/azure/linux.yml
+++ /dev/null
@@ -1,79 +0,0 @@
-parameters:
-  name: ''
-  vmImage: ''
-
-jobs:
-- job: ${{ parameters.name }}
-  pool:
-    vmImage: ${{ parameters.vmImage }}
-  strategy:
-    maxParallel: 11
-    matrix:
-      py27_np_120:
-        ENV_FILE: ci/deps/azure-27-compat.yaml
-        CONDA_PY: "27"
-        PATTERN: "not slow and not network"
-
-      py37_locale:
-        ENV_FILE: ci/deps/azure-37-locale.yaml
-        CONDA_PY: "37"
-        PATTERN: "not slow and not network"
-        LOCALE_OVERRIDE: "zh_CN.UTF-8"
-
-      py36_locale_slow:
-        ENV_FILE: ci/deps/azure-36-locale_slow.yaml
-        CONDA_PY: "36"
-        PATTERN: "not slow and not network"
-        LOCALE_OVERRIDE: "it_IT.UTF-8"
-
-  steps:
-    - script: |
-        if [ "$(uname)" == "Linux" ]; then sudo apt-get install -y libc6-dev-i386; fi
-        echo "Installing Miniconda"{
-        ci/incremental/install_miniconda.sh
-        export PATH=$HOME/miniconda3/bin:$PATH
-        echo "Setting up Conda environment"
-        ci/incremental/setup_conda_environment.sh
-      displayName: 'Before Install'
-    - script: |
-        export PATH=$HOME/miniconda3/bin:$PATH
-        source activate pandas-dev
-        ci/incremental/build.sh
-      displayName: 'Build'
-    - script: |
-        export PATH=$HOME/miniconda3/bin:$PATH
-        source activate pandas-dev
-        ci/run_tests.sh
-      displayName: 'Test'
-    - script: |
-        export PATH=$HOME/miniconda3/bin:$PATH
-        source activate pandas-dev && pushd /tmp && python -c "import pandas; pandas.show_versions();" && popd
-    - task: PublishTestResults@2
-      inputs:
-        testResultsFiles: 'test-data-*.xml'
-        testRunTitle: 'Linux'
-    - powershell: |
-        $junitXml = "test-data-single.xml"
-        $(Get-Content $junitXml | Out-String) -match 'failures="(.*?)"'
-        if ($matches[1] -eq 0)
-        {
-          Write-Host "No test failures in test-data-single"
-        }
-        else
-        {
-          # note that this will produce $LASTEXITCODE=1
-          Write-Error "$($matches[1]) tests failed"
-        }
-
-        $junitXmlMulti = "test-data-multiple.xml"
-        $(Get-Content $junitXmlMulti | Out-String) -match 'failures="(.*?)"'
-        if ($matches[1] -eq 0)
-        {
-          Write-Host "No test failures in test-data-multi"
-        }
-        else
-        {
-          # note that this will produce $LASTEXITCODE=1
-          Write-Error "$($matches[1]) tests failed"
-        }
-      displayName: Check for test failures
diff --git a/ci/azure/macos.yml b/ci/azure/posix.yml
similarity index 69%
rename from ci/azure/macos.yml
rename to ci/azure/posix.yml
index 98409576a5a87..374a82a5ed7d0 100644
--- a/ci/azure/macos.yml
+++ b/ci/azure/posix.yml
@@ -7,12 +7,30 @@ jobs:
   pool:
     vmImage: ${{ parameters.vmImage }}
   strategy:
-    maxParallel: 11
     matrix:
-      py35_np_120:
-        ENV_FILE: ci/deps/azure-macos-35.yaml
-        CONDA_PY: "35"
-        PATTERN: "not slow and not network"
+      ${{ if eq(parameters.name, 'macOS') }}:
+        py35_np_120:
+          ENV_FILE: ci/deps/azure-macos-35.yaml
+          CONDA_PY: "35"
+          PATTERN: "not slow and not network"
+
+      ${{ if eq(parameters.name, 'Linux') }}:
+        py27_np_120:
+          ENV_FILE: ci/deps/azure-27-compat.yaml
+          CONDA_PY: "27"
+          PATTERN: "not slow and not network"
+
+        py37_locale:
+          ENV_FILE: ci/deps/azure-37-locale.yaml
+          CONDA_PY: "37"
+          PATTERN: "not slow and not network"
+          LOCALE_OVERRIDE: "zh_CN.UTF-8"
+
+        py36_locale_slow:
+          ENV_FILE: ci/deps/azure-36-locale_slow.yaml
+          CONDA_PY: "36"
+          PATTERN: "not slow and not network"
+          LOCALE_OVERRIDE: "it_IT.UTF-8"
 
   steps:
     - script: |
@@ -39,7 +57,7 @@ jobs:
     - task: PublishTestResults@2
       inputs:
         testResultsFiles: 'test-data-*.xml'
-        testRunTitle: 'MacOS-35'
+        testRunTitle: ${{ format('{0}-$(CONDA_PY)', parameters.name) }}
     - powershell: |
         $junitXml = "test-data-single.xml"
         $(Get-Content $junitXml | Out-String) -match 'failures="(.*?)"'
diff --git a/ci/azure/windows-py27.yml b/ci/azure/windows-py27.yml
deleted file mode 100644
index 0d9aea816c4ad..0000000000000
--- a/ci/azure/windows-py27.yml
+++ /dev/null
@@ -1,58 +0,0 @@
-parameters:
-  name: ''
-  vmImage: ''
-
-jobs:
-- job: ${{ parameters.name }}
-  pool:
-    vmImage: ${{ parameters.vmImage }}
-  strategy:
-    maxParallel: 11
-    matrix:
-      py36_np121:
-        ENV_FILE: ci/deps/azure-windows-27.yaml
-        CONDA_PY: "27"
-
-  steps:
-    - task: CondaEnvironment@1
-      inputs:
-        updateConda: no
-        packageSpecs: ''
-
-    # Need to install VC 9.0 only for Python 2.7
-    # Once we understand how to do tasks conditional on build matrix variables
-    # we could merge this into azure-windows.yml
-    - powershell: |
-        $wc = New-Object net.webclient
-        $wc.Downloadfile("https://download.microsoft.com/download/7/9/6/796EF2E4-801B-4FC4-AB28-B59FBF6D907B/VCForPython27.msi", "VCForPython27.msi")
-        Start-Process "VCForPython27.msi" /qn -Wait
-      displayName: 'Install VC 9.0'
-
-    - script: |
-        ci\\incremental\\setup_conda_environment.cmd
-      displayName: 'Before Install'
-    - script: |
-        call activate pandas-dev
-        ci\\incremental\\build.cmd
-      displayName: 'Build'
-    - script: |
-        call activate pandas-dev
-        pytest -m "not slow and not network" --junitxml=test-data.xml pandas -n 2 -r sxX --strict --durations=10 %*
-      displayName: 'Test'
-    - task: PublishTestResults@2
-      inputs:
-        testResultsFiles: 'test-data.xml'
-        testRunTitle: 'Windows 27'
-    - powershell: |
-        $junitXml = "test-data.xml"
-        $(Get-Content $junitXml | Out-String) -match 'failures="(.*?)"'
-        if ($matches[1] -eq 0)
-        {
-          Write-Host "No test failures in test-data"
-        }
-        else
-        {
-          # note that this will produce $LASTEXITCODE=1
-          Write-Error "$($matches[1]) tests failed"
-        }
-      displayName: Check for test failures
diff --git a/ci/azure/windows.yml b/ci/azure/windows.yml
index b69c210ca27ba..cece002024936 100644
--- a/ci/azure/windows.yml
+++ b/ci/azure/windows.yml
@@ -7,18 +7,28 @@ jobs:
   pool:
     vmImage: ${{ parameters.vmImage }}
   strategy:
-    maxParallel: 11
     matrix:
       py36_np14:
         ENV_FILE: ci/deps/azure-windows-36.yaml
         CONDA_PY: "36"
 
+      py27_np121:
+        ENV_FILE: ci/deps/azure-windows-27.yaml
+        CONDA_PY: "27"
+
   steps:
     - task: CondaEnvironment@1
       inputs:
         updateConda: no
         packageSpecs: ''
 
+    - powershell: |
+        $wc = New-Object net.webclient
+        $wc.Downloadfile("https://download.microsoft.com/download/7/9/6/796EF2E4-801B-4FC4-AB28-B59FBF6D907B/VCForPython27.msi", "VCForPython27.msi")
+        Start-Process "VCForPython27.msi" /qn -Wait
+      displayName: 'Install VC 9.0 only for Python 2.7'
+      condition: eq(variables.CONDA_PY, '27')
+
     - script: |
         ci\\incremental\\setup_conda_environment.cmd
       displayName: 'Before Install'
@@ -33,7 +43,7 @@ jobs:
     - task: PublishTestResults@2
       inputs:
         testResultsFiles: 'test-data.xml'
-        testRunTitle: 'Windows 36'
+        testRunTitle: 'Windows-$(CONDA_PY)'
     - powershell: |
         $junitXml = "test-data.xml"
         $(Get-Content $junitXml | Out-String) -match 'failures="(.*?)"'