We use USPS shipping for our website. For smaller items that would normally ship First Class, it only returns Priority and Express Mail options. I checked my options and I do have First Class Mail Parcel as a selected option.
Also, a minor annoyance really, when it returns the shipping options, it shows the <sup> and </sup> script.
Do a search for that <sup> and you'll find quite a few posts on how to fix it and also in the extensions section of this website you'll find some vqmods to fix it too (it will give you back your first class option too).