diff --git a/.ci-builds/.azure-exhaustive-tests.yml b/.ci-builds/.azure-exhaustive-tests.yml
index 89470a1c95e..95897029357 100644
--- a/.ci-builds/.azure-exhaustive-tests.yml
+++ b/.ci-builds/.azure-exhaustive-tests.yml
@@ -3,12 +3,6 @@
 # Note: The exhaustive test configuration is in a separate file
 # so that it can be run independently from the regular builds.
 #
-
-resources:
-  - repo: self
-    lfs: true
-    fetchDepth: 1
-
 # Only run the exhaustive tests on the master and maint branches, and
 # also batch up any pending changes so that we will only have at most
 # one build running at a given time (since they take a long time).
@@ -17,7 +11,7 @@ trigger:
   branches:
     include:
     - master
-    - maint/*
+    - maint/maint-*
 
 jobs:
 #-------------------------------------------------------------------------
@@ -30,15 +24,19 @@ jobs:
     vmImage: 'Ubuntu 16.04'
     demands: ant
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - script: |
         echo "Building ICU4J" && cd icu4j && ant init && ant exhaustiveCheck
       displayName: 'Build and Exhaustive Tests'
       env:
         BUILD: ICU4J
     - script: |
-        cat `find out/junit-results -name "*.txt" -exec grep -l FAILED {} \;`
+        [ -d icu4j/out/junit-results ] && cd icu4j && cat `find out/junit-results -name "*.txt" -exec grep -l FAILED {} \;`
       condition: failed() # only run if the build fails.
       displayName: 'List failures (if any)'
+      timeoutInMinutes: 2
 #-------------------------------------------------------------------------
 # Note: The exhaustive tests take roughly 65 mins to complete on the
 # Azure VMs.
@@ -48,6 +46,9 @@ jobs:
   pool:
     vmImage: 'Ubuntu 16.04'
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - script: |
         cd icu4c/source && ./runConfigureICU Linux && make -j2
       displayName: 'Build'
diff --git a/.ci-builds/.azure-pipelines.yml b/.ci-builds/.azure-pipelines.yml
index 3b8de896264..edc9a75ca38 100644
--- a/.ci-builds/.azure-pipelines.yml
+++ b/.ci-builds/.azure-pipelines.yml
@@ -1,10 +1,5 @@
 # Azure Pipelines (VSTS) configuration for CI builds for ICU.
 
-resources:
-  - repo: self
-    lfs: true
-    fetchDepth: 1
-
 jobs:
 #-------------------------------------------------------------------------
 - job: ICU4J_OpenJDK_Ubuntu_1604
@@ -14,13 +9,16 @@ jobs:
     vmImage: 'Ubuntu 16.04'
     demands: ant
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - script: |
         echo "Building ICU4J" && cd icu4j && ant init && ant check 
       displayName: 'Build and Test'
       env:
         BUILD: ICU4J
     - script: |
-        cd icu4j && cat `find out/junit-results -name "*.txt" -exec grep -l FAILED {} \;`
+        [ -d icu4j/out/junit-results ] && cd icu4j && cat `find out/junit-results -name "*.txt" -exec grep -l FAILED {} \;`
       condition: failed() # only run if the build fails.
       displayName: 'List failures (if any)'
 #-------------------------------------------------------------------------
@@ -30,6 +28,9 @@ jobs:
   pool:
     vmImage: 'Ubuntu 16.04'
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - script: |
         cd icu4c/source && ./runConfigureICU Linux && make -j2 check
       displayName: 'Build and Test'
@@ -43,6 +44,9 @@ jobs:
   pool:
     vmImage: 'Ubuntu 16.04'
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - script: |
         export CPPFLAGS="-Werror -Wall -Wextra -Wextra-semi -Wundef -Wnon-virtual-dtor" && cd icu4c/source && ./runConfigureICU Linux && make -j2 tests
       displayName: 'Build only (WarningsAsErrors)'
@@ -56,6 +60,9 @@ jobs:
   pool:
     vmImage: 'Ubuntu 16.04'
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - script: |
         cd icu4c/source && \
         ICU_DATA_FILTER_FILE=../../.ci-builds/data-filter.json ./runConfigureICU Linux && \
@@ -77,6 +84,9 @@ jobs:
       - visualstudio
       - Cmd
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - task: VSBuild@1
       displayName: 'Build Solution'
       inputs:
@@ -111,6 +121,9 @@ jobs:
       - visualstudio
       - Cmd
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - task: VSBuild@1
       displayName: 'Build Solution'
       inputs:
@@ -140,6 +153,9 @@ jobs:
       - visualstudio
       - Cmd
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - task: VSBuild@1
       displayName: 'Build Solution'
       inputs:
@@ -181,6 +197,9 @@ jobs:
       - visualstudio
       - Cmd
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - powershell: |
         $filterPath = $Env:BUILD_SOURCESDIRECTORY + "\.ci-builds\data-filter.json"
         $vstsCommandString = "vso[task.setvariable variable=ICU_DATA_FILTER_FILE]" + $filterPath
@@ -203,6 +222,9 @@ jobs:
       - visualstudio
       - Cmd
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - task: VSBuild@1
       displayName: 'Build Solution'
       inputs:
@@ -228,6 +250,9 @@ jobs:
       - visualstudio
       - Cmd
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - powershell: 'Invoke-WebRequest https://www.python.org/ftp/python/3.7.2/python-3.7.2-amd64-webinstall.exe -OutFile c:\py3-setup.exe'
     - script: |
         c:\py3-setup.exe /quiet PrependPath=1 InstallAllUsers=1 Include_launcher=1 InstallLauncherAllUsers=1 Include_test=0 Include_doc=0 Include_dev=0 Include_debug=0 Include_tcltk=0 TargetDir=c:\py3
@@ -258,6 +283,9 @@ jobs:
     demands:
       - Cmd
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - script: |
        choco install -y msys2
        rem refreshenv
@@ -288,6 +316,9 @@ jobs:
   pool:
     vmImage: 'macOS-10.14'
   steps:
+    - checkout: self
+      lfs: true
+      fetchDepth: 1
     - script: |
         export CPPFLAGS="-Werror -Wall -Wextra -Wextra-semi -Wundef -Wnon-virtual-dtor" && cd icu4c/source && ./runConfigureICU MacOSX && make -j2 tests
       displayName: 'Build only (WarningsAsErrors)'