diff --git a/.azure-pipelines/steps/run.yml b/.azure-pipelines/steps/run.yml
index 015fd83488550..1e49cc00921cd 100644
--- a/.azure-pipelines/steps/run.yml
+++ b/.azure-pipelines/steps/run.yml
@@ -138,43 +138,11 @@ steps:
 
 # Ensure the `aws` CLI is installed so we can deploy later on, cache docker
 # images, etc.
-- bash: |
-    set -e
-    # Temporary code to debug #62967.
-    debug_failed_connections() {
-        echo "trying to ping pypi.org"
-        ping pypi.org -c10 || true
-        echo "trying to ping google.com"
-        ping google.com -c10 || true
-        echo "trying to ping 8.8.8.8"
-        ping 8.8.8.8 -c10 || true
-        echo "trying to download pypi.org"
-        curl https://pypi.org || true
-        echo "trying to download from our S3 bucket"
-        curl https://rust-lang-ci2.s3.amazonaws.com || true
-        echo "trying to dig pypi.org"
-        dig pypi.org || true
-        echo "trying to dig files.pythonhosted.org"
-        dig files.pythonhosted.org || true
-        echo "trying to connect to pypi.org with openssl"
-        echo | openssl s_client -connect pypi.org:443 || true
-        echo "trying to connect to files.pythonhosted.org with openssl"
-        echo | openssl s_client -connect files.pythonhosted.org:443 || true
-    }
-    debug_failed_connections_and_fail() {
-        debug_failed_connections
-        return 1
-    }
-    source src/ci/shared.sh
-    sudo apt-get install -y python3-setuptools
-    debug_failed_connections
-    retry pip3 install -r src/ci/awscli-requirements.txt --upgrade --user || debug_failed_connections_and_fail
-    echo "##vso[task.prependpath]$HOME/.local/bin"
-  displayName: Install awscli (Linux)
-  condition: and(succeeded(), not(variables.SKIP_JOB), eq(variables['Agent.OS'], 'Linux'))
-- script: pip install -r src/ci/awscli-requirements.txt
-  displayName: Install awscli (non-Linux)
-  condition: and(succeeded(), not(variables.SKIP_JOB), ne(variables['Agent.OS'], 'Linux'))
+- bash: src/ci/install-awscli.sh
+  env:
+    AGENT_OS: $(Agent.OS)
+  condition: and(succeeded(), not(variables.SKIP_JOB))
+  displayName: Install awscli
 
 # Configure our CI_JOB_NAME variable which log analyzers can use for the main
 # step to see what's going on.
diff --git a/src/ci/awscli-requirements.txt b/src/ci/awscli-requirements.txt
deleted file mode 100644
index c1ffa525a1b41..0000000000000
--- a/src/ci/awscli-requirements.txt
+++ /dev/null
@@ -1,13 +0,0 @@
-awscli==1.16.201
-botocore==1.12.191
-colorama==0.3.9
-docutils==0.14
-jmespath==0.9.4
-pyasn1==0.4.5
-python-dateutil==2.8.0
-PyYAML==5.1
-rsa==3.4.2
-s3transfer==0.2.1
-six==1.12.0
-urllib3==1.25.3
-futures==3.3.0; python_version < '3.0'
diff --git a/src/ci/install-awscli.sh b/src/ci/install-awscli.sh
new file mode 100755
index 0000000000000..d491b9fbcdcf8
--- /dev/null
+++ b/src/ci/install-awscli.sh
@@ -0,0 +1,35 @@
+#!/bin/bash
+# This script downloads and installs awscli from the packages mirrored in our
+# own S3 bucket. This follows the recommendations at:
+#
+#    https://packaging.python.org/guides/index-mirrors-and-caches/#caching-with-pip
+#
+# To create a new mirrored copy you can run the command:
+#
+#    pip wheel awscli
+#
+# Before compressing please make sure all the wheels end with `-none-any.whl`.
+# If that's not the case you'll need to remove the non-cross-platform ones and
+# replace them with the .tar.gz downloaded from https://pypi.org. Also make
+# sure it's possible to call this script with both Python 2 and Python 3.
+
+set -euo pipefail
+IFS=$'\n\t'
+
+MIRROR="https://rust-lang-ci2.s3.amazonaws.com/rust-ci-mirror/2019-07-27-awscli.tar"
+DEPS_DIR="/tmp/awscli-deps"
+
+pip="pip"
+pipflags=""
+if [[ "${AGENT_OS}" == "Linux" ]]; then
+    pip="pip3"
+    pipflags="--user"
+
+    sudo apt-get install -y python3-setuptools
+    echo "##vso[task.prependpath]$HOME/.local/bin"
+fi
+
+mkdir -p "${DEPS_DIR}"
+curl "${MIRROR}" | tar xf - -C "${DEPS_DIR}"
+"${pip}" install ${pipflags} --no-index "--find-links=${DEPS_DIR}" awscli
+rm -rf "${DEPS_DIR}"