diff --git a/CHANGELOG.md b/CHANGELOG.md
index 18af544..e400cd8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,7 @@
 
 ## Unreleased
 
+- Fix the security update version check message for apps using PyPy (#1040).
 
 ## v175 (2020-08-05)
 
diff --git a/bin/steps/python b/bin/steps/python
index e95b7fc..748bf75 100755
--- a/bin/steps/python
+++ b/bin/steps/python
@@ -8,6 +8,7 @@ PYTHON_VERSION=$(cat runtime.txt)
 VENDORED_PYTHON="${VENDOR_URL}/runtimes/$PYTHON_VERSION.tar.gz"
 
 SECURITY_UPDATE="Python has released a security update! Please consider upgrading to"
+SECURITY_UPDATE_PYPY="The PyPy project has released a security update! Please consider upgrading to"
 
 ONLY_SUPPORTED_2_VERSION="Only the latest version of Python 2 is supported on the platform. Please consider upgrading to"
 
@@ -64,14 +65,14 @@ if curl --output /dev/null --silent --head --fail "$VENDORED_PYTHON"; then
   if [[ "$PYTHON_VERSION" == $PYPY27* ]]; then
     # security update note
     if [ "$PYTHON_VERSION" != "$PYPY_27" ]; then
-      puts-warn "Could not find that Pypy version. Did you mean" "${PYPY_27}?"
+      puts-warn "$SECURITY_UPDATE_PYPY" "$PYPY_27"
       echo "       Learn More: https://devcenter.heroku.com/articles/python-runtimes"
     fi
   fi
   if [[ "$PYTHON_VERSION" == $PYPY36* ]]; then
     # security update note
     if [ "$PYTHON_VERSION" != "$PYPY_36" ]; then
-      puts-warn "Could not find that Pypy version. Did you mean" "${PYPY_36}?"
+      puts-warn "$SECURITY_UPDATE_PYPY" "$PYPY_36"
       echo "       Learn More: https://devcenter.heroku.com/articles/python-runtimes"
     fi
   fi
diff --git a/test/fixtures/pypy2_7/runtime.txt b/test/fixtures/pypy2_7/runtime.txt
index c502b68..e3d29d3 100644
--- a/test/fixtures/pypy2_7/runtime.txt
+++ b/test/fixtures/pypy2_7/runtime.txt
@@ -1 +1 @@
-pypy2.7-7.2.0
+pypy2.7-7.3.1
diff --git a/test/fixtures/pypy2_7_warn/requirements.txt b/test/fixtures/pypy2_7_warn/requirements.txt
new file mode 100644
index 0000000..e69de29
diff --git a/test/fixtures/pypy2_7_warn/runtime.txt b/test/fixtures/pypy2_7_warn/runtime.txt
new file mode 100644
index 0000000..c502b68
--- /dev/null
+++ b/test/fixtures/pypy2_7_warn/runtime.txt
@@ -0,0 +1 @@
+pypy2.7-7.2.0
diff --git a/test/fixtures/pypy3_6/runtime.txt b/test/fixtures/pypy3_6/runtime.txt
index e1af38f..af949aa 100644
--- a/test/fixtures/pypy3_6/runtime.txt
+++ b/test/fixtures/pypy3_6/runtime.txt
@@ -1 +1 @@
-pypy3.6-7.2.0
+pypy3.6-7.3.1
diff --git a/test/fixtures/pypy3_6_warn/requirements.txt b/test/fixtures/pypy3_6_warn/requirements.txt
new file mode 100644
index 0000000..e69de29
diff --git a/test/fixtures/pypy3_6_warn/runtime.txt b/test/fixtures/pypy3_6_warn/runtime.txt
new file mode 100644
index 0000000..e1af38f
--- /dev/null
+++ b/test/fixtures/pypy3_6_warn/runtime.txt
@@ -0,0 +1 @@
+pypy3.6-7.2.0
diff --git a/test/run-versions b/test/run-versions
index c491748..0f76a87 100755
--- a/test/run-versions
+++ b/test/run-versions
@@ -197,24 +197,42 @@ testPython3_8_fail() {
 
 testPypy3_6() {
   compile "pypy3_6"
+  assertCaptured "Installing pypy"
+  assertNotCaptured "security update"
+  assertCaptured "$PYPY_36"
+  assertCaptured "Installing pip 20.1.1, setuptools 47.1.1 and wheel 0.34.2"
+  assertCapturedSuccess
+}
+
+testPypy3_6_warn() {
+  compile "pypy3_6_warn"
   if [[ $STACK = "cedar-14" ]]; then
     assertCapturedError
   else
     assertCaptured "Installing pypy"
+    assertCaptured "security update!"
     assertCaptured "$PYPY_36"
-    assertCaptured "Installing pip 20.1.1, setuptools 47.1.1 and wheel 0.34.2"
     assertCapturedSuccess
   fi
 }
 
 testPypy2_7() {
   compile "pypy2_7"
+  assertCaptured "Installing pypy"
+  assertNotCaptured "security update"
+  assertCaptured "$PYPY_27"
+  assertCaptured "Installing pip 20.1.1, setuptools 44.1.1 and wheel 0.34.2"
+  assertCapturedSuccess
+}
+
+testPypy2_7_warn() {
+  compile "pypy2_7_warn"
   if [[ $STACK = "cedar-14" ]]; then
     assertCapturedError
   else
     assertCaptured "Installing pypy"
+    assertCaptured "security update!"
     assertCaptured "$PYPY_27"
-    assertCaptured "Installing pip 20.1.1, setuptools 44.1.1 and wheel 0.34.2"
     assertCapturedSuccess
   fi
 }