<div id="divStuff" runat="server" Visible="False"
                                    style="float: left; position: relative; padding-top: 5px; padding-left: 25px; height: 340px; width: 500px; margin-right: 2px" >
                                    <fieldset style="height: 350px">
                                        <legend><b>Names</b></legend>
                                        <div style="padding-top: 25px; padding-left: 15px">
                                            <div style="float: left;padding-left: 40px">
                                                <div>
                                                    <asp:Label runat="server" Text="Available" Font-Bold="True"></asp:Label>
                                                </div>
                     <telerik:RadListBox id="lstAvailableNames"
                                                    AllowTransfer="true" TransferToID="lstSelectedNames" AllowReorder="True" ButtonSettings-AreaWidth="35px"
                                                    TransferMode="Move" SelectionMode="Multiple" Sort="Ascending"
                      runat="server" Height="260px" Width="185px" AutoPostBackOnTransfer="True"
                                                    OnTransferred="OnListBoxTransferred">
                     </telerik:RadListBox>
                                            </div>
                                            <div style="float: left">
                                                <div>
                                                <asp:Label runat="server" Text="Selected" Font-Bold="True"></asp:Label>
                                                </div>
                     <telerik:RadListBox  id="lstSelectedNames" SelectionMode="Multiple"
                                                    ButtonSettings-AreaWidth="35px" Sort="Ascending"
                      runat="server" Height="260px" Width="155px" >
                     </telerik:RadListBox>
                                            </div>
                                        </div>
                                    </fieldset>
                                </div>

Hello Phil,

I tested using the markup you sent, but I was not able to reproduce the issue. I took a screen-shot showing how the page is displayed at my side in Firefox browser(I tested with 2015.2.623 version of Telerik UI for ASP.NET AJAX).

Attached you may find the project I tested with. Please inspect it at your side and modify it in order to show me what I am missing to reproduce the problem.

Regards,
Aneliya Petkova
Telerik