diff --git a/tests/bugs/when-mistaking-argument-of-strings/test.sh b/tests/bugs/when-mistaking-argument-of-strings/test.sh
index 5dd4033..b2ebef1 100755
--- a/tests/bugs/when-mistaking-argument-of-strings/test.sh
+++ b/tests/bugs/when-mistaking-argument-of-strings/test.sh
@@ -41,12 +41,20 @@ rlJournalStart
 
     rlPhaseStartTest "#3: strings -n 0"
         rlRun "strings -n 0 2>&1 | tee output"
-        rlAssertGrep "invalid minimum string length 0" output
+        if rlIsFedora "> 39"; then
+            rlAssertGrep "minimum string length is too small: 0" output
+        else
+            rlAssertGrep "invalid minimum string length 0" output
+        fi
     rlPhaseEnd
 
     rlPhaseStartTest "#4: strings --bytes 0"
         rlRun "strings --bytes 0 2>&1 | tee output"
-        rlAssertGrep "invalid minimum string length 0" output
+        if rlIsFedora "> 39"; then
+            rlAssertGrep "minimum string length is too small: 0" output
+        else
+            rlAssertGrep "invalid minimum string length 0" output
+        fi
     rlPhaseEnd
 
     rlPhaseStartCleanup
diff --git a/tests/rebuilds/wget/main.fmf b/tests/rebuilds/wget/main.fmf
index 8ee8938..a7ef164 100644
--- a/tests/rebuilds/wget/main.fmf
+++ b/tests/rebuilds/wget/main.fmf
@@ -7,3 +7,16 @@ tag+:
 
 require+:
   - wget
+
+environment+:
+  WGET_PACKAGE: "wget"
+  REQUIRES: "wget"
+
+adjust+:
+  - when: distro >= fedora-39
+    require+:
+      - wget2
+
+    environment+:
+      WGET_PACKAGE: "wget2"
+      REQUIRES: "wget2"
diff --git a/tests/rebuilds/wget/test.sh b/tests/rebuilds/wget/test.sh
index 04533b3..b0dea4e 100755
--- a/tests/rebuilds/wget/test.sh
+++ b/tests/rebuilds/wget/test.sh
@@ -35,9 +35,11 @@ rlJournalStart
     rlPhaseStartSetup
         buTestHeader
 
+        rlLogInfo "WGET_PACKAGE=$WGET_PACKAGE"
+
         buEnterTmpDir
 
-        buPrepareSRPM "wget"
+        buPrepareSRPM "$WGET_PACKAGE"
     rlPhaseEnd
 
     rlPhaseStartTest