diff --git a/IPython/html/static/base/less/page.less b/IPython/html/static/base/less/page.less
index ddc7d98..56533dd 100644
--- a/IPython/html/static/base/less/page.less
+++ b/IPython/html/static/base/less/page.less
@@ -120,9 +120,11 @@ span#login_widget > .button,
 // class for stretching dialogs to fill the screen
 .modal_stretch .modal-dialog {
     .vbox();
-    min-height: 80%;
+    min-height: 80vh;
     .modal-body {
-        max-height: none;
+        // ~"foo" is to avoid less turning this into a weird value
+        max-height: calc(~"100vh - 200px");
+        overflow: auto;
         flex: 1;
     }
 }
diff --git a/IPython/html/static/style/style.min.css b/IPython/html/static/style/style.min.css
index db72a44..c4608ca 100644
--- a/IPython/html/static/style/style.min.css
+++ b/IPython/html/static/style/style.min.css
@@ -8572,10 +8572,11 @@ span#login_widget > .button .badge,
   display: flex;
   flex-direction: column;
   align-items: stretch;
-  min-height: 80%;
+  min-height: 80vh;
 }
 .modal_stretch .modal-dialog .modal-body {
-  max-height: none;
+  max-height: calc(100vh - 200px);
+  overflow: auto;
   flex: 1;
 }
 @media (min-width: 768px) {