diff --git a/frontend_tests/node_tests/copy_and_paste.js b/frontend_tests/node_tests/copy_and_paste.js
index d5b5952644..38a9d332a9 100644
--- a/frontend_tests/node_tests/copy_and_paste.js
+++ b/frontend_tests/node_tests/copy_and_paste.js
@@ -33,4 +33,12 @@ var copy_and_paste = zrequire('copy_and_paste');
     // and the '  \n' is a bit strange as well
     assert.equal(copy_and_paste.paste_handler_converter(input),
                  '  \n1\\. text');
+
+    input = '
Zulip overview
';
+    assert.equal(copy_and_paste.paste_handler_converter(input),
+                 'Zulip overview');
+
+    input = 'This text is italic';
+    assert.equal(copy_and_paste.paste_handler_converter(input),
+                 '*This text is italic*');
 }());
diff --git a/static/js/copy_and_paste.js b/static/js/copy_and_paste.js
index acbf8e6716..b35961425b 100644
--- a/static/js/copy_and_paste.js
+++ b/static/js/copy_and_paste.js
@@ -141,7 +141,24 @@ function copy_handler() {
 }
 
 exports.paste_handler_converter = function (paste_html) {
-    var markdown_html = toMarkdown(paste_html);
+    var converters = {
+        converters: [
+            {
+                filter: ['h1', 'h2', 'h3', 'h4', 'h5', 'h6'],
+                replacement: function (content) {
+                    return content;
+                },
+            },
+
+            {
+                filter: ['em', 'i'],
+                replacement: function (content) {
+                    return '*' + content + '*';
+                },
+            },
+        ],
+    };
+    var markdown_html = toMarkdown(paste_html, converters);
 
     // Now that we've done the main conversion, we want to remove
     // any HTML tags that weren't converted to markdown-style