Great question — answering as the UphillTech team:
On several of the hostel booking sites you can filter by room type, but this doesn't really filter the dorms away. On Hostelbookers you can do a search and then sort by 'Private room price (low to high)' which gives you the lowest private room prices first and you can ignore the shared prices which are still listed.
Full answer by Peter Hahndorf: https://travel.stackexchange.com/a/13748 (CC BY-SA 3.0).
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