Have tested with the inserts and some covers.
The slimmest insert is for phone without case (screen protectors are fine) and will fit nicely.
The 2nd insert allows for thin cases - like the elecom ones http://www.elecom.com.tw/prod-1.asp?id=2115. These will fit without removing the cover.
alternately, you could use it without inserts - but i found it does not hold the phone well. Maybe a simple DIY hack ( stick a flat lego brick or something at the back ) may help a better fit.