I recently started running into storage space issues related to maintaining full copies of the Ethereum block chain on my SSD. A quick google showed a lot of people having the same issue. With Parity's release of version 1.7, they now support running the client in "light mode" but state that it is not integrated with the ui. I personally like the in-browser interface and believe that after a little trial and error I have been able to get it working. Here is how I did it:

Following Parity's configuration instructions (https://github.com/paritytech/parity/wiki/Configuring-Parity), I created a config.toml file using notepad and save it to the following directory: 

%UserProfile%\AppData\Roaming\Parity\Ethereum\config.toml

Instead of going through the entire config generator process, I simply had the config.toml file contain the following text:
______________
[parity]

light = true
______________


After that, you can run the desktop shortcut as usual. It significantly reduced the size of the blockchain data on my SSD. Hope this helps.