You don't have to support all the way back to 2.2 if it's too much trouble given your resources. Designing for 4.0+ will already give you more than 80% of the market, [1] and the 20% that you are excluding are the most likely to be underpowered and cause 80% of the device-specific glitches you would find in the wild.

[1] https://developer.android.com/about/dashboards/index.html