diff --git a/Jenkinsfile-dynamatrix b/Jenkinsfile-dynamatrix
index 11e14f15bf..0dbcb21abc 100644
--- a/Jenkinsfile-dynamatrix
+++ b/Jenkinsfile-dynamatrix
@@ -478,8 +478,8 @@ set | sort -n """
                     // BUILD_TYPE=default-tgt:distcheck-light + NO_PKG_CONFIG=true ?
                     ],
                 dynamatrixAxesCommonEnv: [
-                    ['LANG=C','LC_ALL=C','TZ=UTC'
-                     //,'BUILD_WARNFATAL=yes','BUILD_WARNOPT=hard'
+                    ['LANG=C','LC_ALL=C','TZ=UTC','BUILD_WARNFATAL=yes'
+                     //,'BUILD_WARNOPT=hard'
                     ]
                     ],
                 allowedFailure: [
@@ -527,8 +527,8 @@ set | sort -n """
                     'BUILD_TYPE': ['default-tgt:cppcheck']
                     ],
                 dynamatrixAxesCommonEnv: [
-                    ['LANG=C','LC_ALL=C','TZ=UTC', 'DO_CLEAN_CHECK=no'
-                     //,'BUILD_WARNFATAL=yes','BUILD_WARNOPT=hard'
+                    ['LANG=C','LC_ALL=C','TZ=UTC', 'DO_CLEAN_CHECK=no', 'BUILD_WARNFATAL=yes'
+                     //,'BUILD_WARNOPT=hard'
                     ]
                     ],
                 allowedFailure: [
@@ -685,7 +685,8 @@ set | sort -n """
                     ],
                 dynamatrixAxesCommonEnv: [
                     ['LANG=C','LC_ALL=C','TZ=UTC',
-                     'BUILD_WARNFATAL=yes','BUILD_WARNOPT=minimal'
+                     'BUILD_WARNFATAL=yes'
+                     //,'BUILD_WARNOPT=medium'
                     ]
                     ],
                 allowedFailure: [
@@ -726,9 +727,14 @@ set | sort -n """
                 dynamatrixAxesCommonEnv: [
                     ['LANG=C','LC_ALL=C','TZ=UTC',
                      // Build in a subdirectory to check that out-of-dir
-                     // builds are healthy too
+                     // builds are healthy too.
+                     // NOTE: It would be useful to also have a recipe to build
+                     // "completely out-of-tree", in a different filesystem (to
+                     // make sure we do not rely on hard-links, relative paths,
+                     // etc.)
                      'CI_BUILDDIR=obj',
-                     'BUILD_WARNFATAL=yes','BUILD_WARNOPT=minimal'
+                     'BUILD_WARNFATAL=yes'
+                     //,'BUILD_WARNOPT=minimal'
                     ]
                     ],
                 allowedFailure: [
@@ -767,7 +773,8 @@ set | sort -n """
                     ],
                 dynamatrixAxesCommonEnv: [
                     ['LANG=C','LC_ALL=C','TZ=UTC',
-                     'BUILD_WARNFATAL=yes','BUILD_WARNOPT=minimal'
+                     'BUILD_WARNFATAL=yes'
+                     //,'BUILD_WARNOPT=minimal'
                     ]
                     ],
                 allowedFailure: [
@@ -1213,7 +1220,7 @@ set | sort -n """
         'bodyParStages': dynacfgPipeline.slowBuildDefaultBody_ci_build
         ] // one slowBuild filter configuration
 
-        ,[name: 'Strict C and GNU standard builds on cross-Windows platforms (Linux+mingw), without distcheck and docs (allowed to fail)',
+        ,[name: (dynacfgPipeline.disableStrictCIBuild_CrossWindows ? '' : 'Strict C and ') + 'GNU standard builds on cross-Windows platforms (Linux+mingw), without distcheck and docs (allowed to fail)',
          disabled: dynacfgPipeline.disableSlowBuildCIBuild,
          //branchRegexSource: ~/^(PR-.+|.*fightwarn.*|.*Windows.*)$/,
          //branchRegexTarget: ~/fightwarn|Windows-.*/,