Do you want a drop-down list or a listbox? I think you need the size attribute in order to generate a listbox. Then there should be a scroll bar if the number of options exceeds size. For a drop-down list, I think there might need to be 20 items before you get a scroll bar.

https://developer.mozilla.org/en/HTML/Element/select

Edit: Actually, on this demo page, adding multiple="multiple" to the select tag generates a listbox. If I add size="2" then the lower two options are hidden and the scroll arrows flip the bottom or top two options into and out of view.

http://www.w3schools.com/tags/tryit.asp?filename=tryhtml_option

Edit: I think I have a better idea what you meant: when the scrollbar is smaller than size="4" there is no "thumb" on the scrollbar to move up and down. I think that's because the scrollbar is too short.

Thank you for your reply but the last edit I think is nearest the point. However, only Firefox seems to have this difficulty and the whole scrollbar disappears. I will try and supply a complete example in straight html. Maybe screen resolution or some other customization was not taken into account in their design.

I have done some testing with:

<select  name="Select1" size="2" multiple="multiple">
 <option>Rabbits</option>
 <option>Dogs</option>
 <option>Cats</option>
 <option>Haddock</option>
 <option>Shark</option>
 <option>Pig</option>
 <option>Cow</option>
 <option>Horse</option>
 </select>

and found that only IE8 is correct and consistent in this respect, Chrome tends to increase the value of size in some arbitary way whilst Firefox 14.01, unlike IE and Chrome, does not supply any scrollbar to scroll through the options. (even though the size is correct) Increasing the size to 3 puts back the scrollbar in Firefox.

I have a problem with "select" in FF 14.0.1 under ubuntu. After I added options in my select, on my page I can't change scroll options. My select is just fixed, not scrollable, though under W7 this version of FF works normally with select.