diff --git a/lib/yui/build/moodle-core-tooltip/moodle-core-tooltip.js b/lib/yui/build/moodle-core-tooltip/moodle-core-tooltip.js
index 2d1ce55bc32..508070410af 100644
--- a/lib/yui/build/moodle-core-tooltip/moodle-core-tooltip.js
+++ b/lib/yui/build/moodle-core-tooltip/moodle-core-tooltip.js
@@ -252,8 +252,7 @@ YUI.add('moodle-core-tooltip', function (Y, NAME) {
             this.setAttrs({
                 headerContent: this.get('initialheadertext'),
                 bodyContent: this.get('initialbodytext'),
-                footerContent: this.get('initialfootertext'),
-                zIndex: 150
+                footerContent: this.get('initialfootertext')
             });
 
             // Hide and then render the dialogue.
@@ -263,6 +262,10 @@ YUI.add('moodle-core-tooltip', function (Y, NAME) {
             // Hook into a few useful areas.
             this.bb = this.get('boundingBox');
 
+            // Add an additional class to the boundingbox to allow tooltip-specific style to be
+            // set.
+            this.bb.addClass('moodle-dialogue-tooltip');
+
             // Change the alignment if this is an RTL language.
             if (right_to_left()) {
                 this.alignpoints = [
diff --git a/theme/base/style/core.css b/theme/base/style/core.css
index 8d176449218..6d50030aca2 100644
--- a/theme/base/style/core.css
+++ b/theme/base/style/core.css
@@ -1020,7 +1020,9 @@ sup {vertical-align: super;}
 .moodle-dialogue .tooltiptext {
     max-height: 300px;
 }
-
+.moodle-dialogue-base .moodle-dialogue.moodle-dialogue-tooltip {
+    z-index: 3001;
+}
 
 /* Question Bank - Question Chooser "Close" button */
 #page-question-edit.dir-rtl a.container-close {right:auto;left:6px;}