diff --git a/.appveyor.yml b/.appveyor.yml
index 07ba574f4e..296678990f 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -83,8 +83,8 @@ build_script:
              # configure its flags. liblzma just works.
              #>
             Execute-Bash "ZSTD_CFLAGS='-L/${env:compiler_path}/include' ZSTD_LIBS='-L/${env:compiler_path}/lib -lzstd' ../configure --prefix=/${env:compiler_path} --build=${env:target} --host=${env:target} --with-openssl-dir=/${env:compiler_path} --disable-asciidoc --enable-fatal-warnings ${env:hardening}"
-            Execute-Bash "V=1 make -j2"
-            Execute-Bash "V=1 make -j2 install"
+            Execute-Bash "V=1 make -k -j2"
+            Execute-Bash "V=1 make -k -j2 install"
      }
 
 test_script:
@@ -97,7 +97,7 @@ test_script:
             Set-Location "${env:build}"
             Copy-Item "C:/msys64/${env:compiler_path}/bin/libssp-0.dll" -Destination "${env:build}/src/test"
             Copy-Item "C:/msys64/${env:compiler_path}/bin/zlib1.dll" -Destination "${env:build}/src/test"
-            Execute-Bash "VERBOSE=1 make -j2 check"
+            Execute-Bash "VERBOSE=1 make -k -j2 check"
     }
 
 on_finish:
diff --git a/.travis.yml b/.travis.yml
index 221fab71c6..7347ae5dfe 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -20,8 +20,10 @@ os:
 ## Instead, we list each job under matrix: include:
 env:
   global:
-    ## The Travis CI environment allows us two cores, so let's use both.
-    - MAKEFLAGS="-j 2"
+    ## The Travis CI environment allows us two cores, so let's use both.  Also,
+    ## let's use the "-k" flag so that we get all of the compilation failures,
+    ## not just the first one.
+    - MAKEFLAGS="-k -j 2"
     ## We turn on hardening by default
     ## Also known as --enable-fragile-hardening in 0.3.0.3-alpha and later
     - HARDENING_OPTIONS="--enable-expensive-hardening"
diff --git a/changes/ticket31372_appveyor b/changes/ticket31372_appveyor
new file mode 100644
index 0000000000..e7bb03182e
--- /dev/null
+++ b/changes/ticket31372_appveyor
@@ -0,0 +1,4 @@
+  o Minor features (continuous integration):
+    - When building on Appveyor, pass the "-k" flag to make, so that
+      we are informed of all compilation failures, not just the first
+      one or two. Closes part of ticket 31372.
diff --git a/changes/ticket31372_travis b/changes/ticket31372_travis
new file mode 100644
index 0000000000..403869b2ed
--- /dev/null
+++ b/changes/ticket31372_travis
@@ -0,0 +1,4 @@
+  o Minor features (continuous integration):
+    - When building on Travis, pass the "-k" flag to make, so that
+      we are informed of all compilation failures, not just the first
+      one or two. Closes part of ticket 31372.