diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index a02f33d4f1..25d5adb5ee 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -474,7 +474,7 @@ tarball-create:
   only:
     - tags
 
-# Jobs for doc builds on Debian Sid (amd64)
+# Jobs for doc builds on Debian 10 "buster" (amd64)
 
 docs:
   <<: *release_branch_triggering_rules
@@ -608,7 +608,7 @@ unit:gcc:centos8:amd64:
     - job: gcc:centos8:amd64
       artifacts: true
 
-# Jobs for regular GCC builds on Debian 9 Stretch (amd64)
+# Jobs for regular GCC builds on Debian 9 "stretch" (amd64)
 
 gcc:stretch:amd64:
   variables:
@@ -631,7 +631,7 @@ unit:gcc:stretch:amd64:
     - job: gcc:stretch:amd64
       artifacts: true
 
-# Jobs for regular GCC builds on Debian 10 Buster (amd64)
+# Jobs for regular GCC builds on Debian 10 "buster" (amd64)
 
 gcc:buster:amd64:
   variables:
@@ -654,7 +654,7 @@ unit:gcc:buster:amd64:
     - job: gcc:buster:amd64
       artifacts: true
 
-# Jobs for scan-build builds on Debian Buster (amd64)
+# Jobs for scan-build builds on Debian 10 "buster" (amd64)
 
 .scan_build: &scan_build |
   ${SCAN_BUILD} --html-title="BIND 9 ($CI_COMMIT_SHORT_SHA)" \
@@ -685,7 +685,7 @@ scan-build:
     expire_in: "1 day"
     when: on_failure
 
-# Jobs for regular GCC builds on Debian Sid (amd64)
+# Jobs for regular GCC builds on Debian "sid" (amd64)
 # Also tests configration option: --without-lmdb.
 
 gcc:sid:amd64:
@@ -715,7 +715,7 @@ cppcheck:
   <<: *base_image
   <<: *cppcheck_job
 
-# Job for out-of-tree GCC build on Debian Sid (amd64)
+# Job for out-of-tree GCC build on Debian "sid" (amd64)
 # Also tests configration option: --with-lmdb.
 
 gcc:out-of-tree:
@@ -729,7 +729,7 @@ gcc:out-of-tree:
   <<: *base_image
   <<: *build_job
 
-# Jobs for tarball GCC builds on Debian Sid (amd64)
+# Jobs for tarball GCC builds on Debian 10 "buster" (amd64)
 
 gcc:tarball:
   variables:
@@ -771,7 +771,7 @@ unit:gcc:tarball:
   only:
     - tags
 
-# Jobs for regular GCC builds on Debian Sid (arm64)
+# Jobs for regular GCC builds on Debian "sid" (arm64)
 
 gcc:sid:arm64:
   variables:
@@ -795,7 +795,7 @@ unit:gcc:sid:arm64:
     - job: gcc:sid:arm64
       artifacts: true
 
-# Jobs for regular GCC builds on Debian Sid (i386)
+# Jobs for regular GCC builds on Debian "sid" (i386)
 
 gcc:sid:i386:
   variables:
@@ -843,30 +843,6 @@ unit:gcc:tumbleweed:amd64:
     - job: gcc:tumbleweed:amd64
       artifacts: true
 
-# Jobs for regular GCC builds on Fedora 31 (amd64)
-
-gcc:fedora31:amd64:
-  variables:
-    CC: gcc
-    CFLAGS: "${CFLAGS_COMMON} -O1"
-    EXTRA_CONFIGURE: "--with-libidn2"
-  <<: *fedora_31_amd64_image
-  <<: *build_job
-
-system:gcc:fedora31:amd64:
-  <<: *fedora_31_amd64_image
-  <<: *system_test_job
-  needs:
-    - job: gcc:fedora31:amd64
-      artifacts: true
-
-unit:gcc:fedora31:amd64:
-  <<: *fedora_31_amd64_image
-  <<: *unit_test_job
-  needs:
-    - job: gcc:fedora31:amd64
-      artifacts: true
-
 # Jobs for regular GCC builds on Ubuntu 16.04 Xenial Xerus (amd64)
 
 gcc:xenial:amd64:
@@ -915,7 +891,7 @@ unit:gcc:bionic:amd64:
     - job: gcc:bionic:amd64
       artifacts: true
 
-# Jobs for builds with ASAN enabled
+# Jobs for ASAN builds on Debian 10 "buster" (amd64)
 
 gcc:asan:
   variables:
@@ -971,7 +947,7 @@ unit:clang:asan:
     - job: clang:asan
       artifacts: true
 
-# Jobs for builds with TSAN enabled
+# Jobs for TSAN builds on Debian 10 "buster" (amd64)
 
 gcc:tsan:
   <<: *base_image
@@ -1027,7 +1003,8 @@ unit:clang:tsan:
     - job: clang:tsan
       artifacts: true
 
-# Jobs for mutex-based atomics on Debian SID (amd64)
+# Jobs for builds with mutex-based atomics on Debian 10 "buster" (amd64)
+
 gcc:mutexatomics:
   variables:
     CC: gcc
@@ -1050,7 +1027,7 @@ unit:gcc:mutexatomics:
     - job: gcc:mutexatomics
       artifacts: true
 
-# Jobs for Clang builds on Debian Buster (amd64)
+# Jobs for Clang builds on Debian 10 "buster" (amd64)
 
 clang:buster:amd64:
   variables:
@@ -1074,9 +1051,9 @@ unit:clang:buster:amd64:
     - job: clang:buster:amd64
       artifacts: true
 
-# Jobs for PKCS#11-enabled GCC builds on Debian Sid (amd64)
+# Jobs for PKCS#11-enabled GCC builds on Debian "sid" (amd64)
 
-gcc:pkcs11:
+gcc:softhsm2.4:
   variables:
     CC: gcc
     CFLAGS: "${CFLAGS_COMMON}"
@@ -1084,18 +1061,42 @@ gcc:pkcs11:
   <<: *base_image
   <<: *build_job
 
-system:gcc:pkcs11:
+system:gcc:softhsm2.4:
   <<: *base_image
   <<: *system_test_job
   needs:
-    - job: gcc:pkcs11
+    - job: gcc:softhsm2.4
       artifacts: true
 
-unit:gcc:pkcs11:
+unit:gcc:softhsm2.4:
   <<: *base_image
   <<: *unit_test_job
   needs:
-    - job: gcc:pkcs11
+    - job: gcc:softhsm2.4
+      artifacts: true
+
+# Jobs for PKCS#11-enabled GCC builds on Fedora 31 (amd64)
+
+gcc:softhsm2.6:
+  variables:
+    CC: gcc
+    CFLAGS: "${CFLAGS_COMMON} -O1"
+    EXTRA_CONFIGURE: "--with-libidn2 --enable-native-pkcs11 --with-pkcs11=/usr/lib64/pkcs11/libsofthsm2.so"
+  <<: *fedora_31_amd64_image
+  <<: *build_job
+
+system:gcc:softhsm2.6:
+  <<: *fedora_31_amd64_image
+  <<: *system_test_job
+  needs:
+    - job: gcc:softhsm2.6
+      artifacts: true
+
+unit:gcc:softhsm2.6:
+  <<: *fedora_31_amd64_image
+  <<: *unit_test_job
+  needs:
+    - job: gcc:softhsm2.6
       artifacts: true
 
 # Jobs for Clang builds on FreeBSD 11.3 (amd64)