page layout - InDesign Data Merge and hiding missing data

I have an InDesign document which is filled from the data in a CSV using data mrege. The csv has columns for name, phone, email etc, but some of the data in the csv isn't filled in as it is not all necessary so when InDesign gets to that record it leaves it blank. So far so good, but I have my document setup like this:

Name: Bob


Phone: 01234567890

Email: bob @ email .com

When a field is missing I end up with just a blank record and I want the data merge or a script to just hide that all together if it's missing so that if a phone number is missing I just get:

Name: Bob

Email: bob @ email .com

and not:

Name: Bob

Phone:  

Email: bob @ email .com

I can't find any way of doing it, except by manually going through the generated document and that is more open to error.