diff --git a/testssl.sh b/testssl.sh
index 362fc57..e32cdfb 100755
--- a/testssl.sh
+++ b/testssl.sh
@@ -1977,7 +1977,7 @@ check_revocation_ocsp() {
           if [[ "$OSSL_NAME" =~ LibreSSL ]]; then
                host_header="-header Host ${host_header}"
           elif [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 1.1.0* ]] || [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 1.1.1* ]] || \
-               [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 3.0.0* ]]; then
+               [[ $OSSL_VER_MAJOR == 3 ]]; then
                host_header="-header Host=${host_header}"
           else
                host_header="-header Host ${host_header}"
@@ -4256,7 +4256,7 @@ ciphers_by_strength() {
                ossl_ciphers_proto=""
           elif [[ $proto == -ssl2 ]] || [[ $proto == -ssl3 ]] || \
                [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 1.1.0* ]] || [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 1.1.1* ]] || \
-               [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 3.0.0* ]]; then
+               [[ $OSSL_VER_MAJOR == 3 ]]; then
                ossl_ciphers_proto="$proto"
           else
                ossl_ciphers_proto="-tls1"
@@ -6482,7 +6482,7 @@ sub_session_resumption() {
           return 7
      fi
      if "$byID" && [[ ! "$OSSL_NAME" =~ LibreSSL ]] && \
-        ( [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 1.1.1* ]] || [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 3.0.0* ]] ) && \
+        ( [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 1.1.1* ]] || [[ $OSSL_VER_MAJOR == 3 ]] ) && \
         [[ ! -s "$sess_data" ]]; then
           # it seems OpenSSL indicates no Session ID resumption by just not generating output
           debugme echo -n "No session resumption byID (empty file)"
@@ -11670,7 +11670,7 @@ hmac() {
      local key="$2" text="$3" output
      local -i ret
 
-     if [[ ! "$OSSL_NAME" =~ LibreSSL ]] && [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 3.0.0* ]]; then
+     if [[ ! "$OSSL_NAME" =~ LibreSSL ]] && [[ $OSSL_VER_MAJOR == 3 ]]; then
           output="$(hex2binary "$text" | $OPENSSL mac -macopt digest:"${hash_fn/-/}" -macopt hexkey:"$key" HMAC 2>/dev/null)"
           ret=$?
           tm_out "$(strip_lf "$output")"
@@ -11691,7 +11691,7 @@ hmac-transcript() {
      local key="$2" transcript="$3" output
      local -i ret
 
-     if [[ ! "$OSSL_NAME" =~ LibreSSL ]] && [[ $OSSL_VER_MAJOR.$OSSL_VER_MINOR == 3.0.0* ]]; then
+     if [[ ! "$OSSL_NAME" =~ LibreSSL ]] && [[ $OSSL_VER_MAJOR == 3 ]]; then
           output="$(hex2binary "$transcript" | \
                     $OPENSSL dgst "$hash_fn" -binary 2>/dev/null | \
                     $OPENSSL mac -macopt digest:"${hash_fn/-/}" -macopt hexkey:"$key" HMAC 2>/dev/null)"
@@ -19329,7 +19329,7 @@ find_openssl_binary() {
 
      # see #190, reverting logic: unless otherwise proved openssl has no dh bits
      case "$OSSL_VER_MAJOR.$OSSL_VER_MINOR" in
-          1.0.2|1.1.0|1.1.1|3.0.0) HAS_DH_BITS=true ;;
+          1.0.2|1.1.0|1.1.1|3.*) HAS_DH_BITS=true ;;
      esac
      if [[ "$OSSL_NAME" =~ LibreSSL ]]; then
           [[ ${OSSL_VER//./} -ge 210 ]] && HAS_DH_BITS=true
@@ -19463,7 +19463,7 @@ find_openssl_binary() {
      # not check /usr/bin/openssl -- if available. This is more a kludge which we shouldn't use for
      # every openssl feature. At some point we need to decide which with openssl version we go.
      OPENSSL2=/usr/bin/openssl
-     if [[ ! $OSSL_VER =~ 1.1.1 ]] && [[ ! $OSSL_VER_MAJOR =~ 3 ]]; then
+     if [[ ! "$OSSL_NAME" =~ LibreSSL ]] && [[ ! $OSSL_VER =~ 1.1.1 ]] && [[ ! $OSSL_VER_MAJOR =~ 3 ]]; then
           if [[ -x $OPENSSL2 ]]; then
                $OPENSSL2 s_client -help 2>$s_client_has2
                $OPENSSL2 s_client -starttls foo 2>$s_client_starttls_has2