diff --git a/tests/bugs/when-mistaking-argument-of-strings/test.sh b/tests/bugs/when-mistaking-argument-of-strings/test.sh
index aa02bb9..6f52627 100755
--- a/tests/bugs/when-mistaking-argument-of-strings/test.sh
+++ b/tests/bugs/when-mistaking-argument-of-strings/test.sh
@@ -47,6 +47,9 @@ rlJournalStart
         elif rlIsCentOS ">= 10"; then
             rlAssertGrep "minimum string length is too small: 0" output
 
+        elif rlIsRHEL ">= 10"; then
+            rlAssertGrep "minimum string length is too small: 0" output
+
         else
             rlAssertGrep "invalid minimum string length 0" output
         fi
@@ -60,6 +63,9 @@ rlJournalStart
         elif rlIsCentOS ">= 10"; then
             rlAssertGrep "minimum string length is too small: 0" output
 
+        elif rlIsRHEL ">= 10"; then
+            rlAssertGrep "minimum string length is too small: 0" output
+
         else
             rlAssertGrep "invalid minimum string length 0" output
         fi
diff --git a/tests/rebuilds/kernel/main.fmf b/tests/rebuilds/kernel/main.fmf
index 84e54bc..50bef39 100644
--- a/tests/rebuilds/kernel/main.fmf
+++ b/tests/rebuilds/kernel/main.fmf
@@ -66,8 +66,8 @@ adjust+:
     require+:
       - pesign
 
-  - because: "unifdef is available with RHEL-8.9 and newer"
-    when: distro >= rhel-8.9
+  - because: "unifdef is available with RHEL-8.9 and newer and not in RHEL-10"
+    when: distro >= rhel-8.9 and distro != rhel-10
     require+:
       - unifdef
 
diff --git a/tests/testsuite/main.fmf b/tests/testsuite/main.fmf
index 3868add..330d252 100644
--- a/tests/testsuite/main.fmf
+++ b/tests/testsuite/main.fmf
@@ -11,13 +11,21 @@ require+:
   - dejagnu
   - bison
   - flex
-  - zlib-static
   - sharutils
   - yum-utils
   - libstdc++-static
   - rpm-build
 
 adjust+:
+  - because: "On RHEL-10, zlib-static is missing"
+    when: distro != rhel-10
+    require+:
+      - zlib-static
+
+  - because: "On RHEL-10 and newer, system binutils build extra binaries for cross compilation"
+    when: distro >= rhel-10 and collection is not defined
+    test: "$WITH_SCL ./test-with-cross.sh"
+
   - because: "On RHEL-9.3.0 and newer, system binutils build extra binaries for cross compilation"
     when: distro == rhel-9.3 and collection is not defined
     test: "$WITH_SCL ./test-with-cross.sh"