My straight-frame Birdy was under 20 lbs. Swapping out the heavy original crankset and bottom bracket made a significant difference, lighter hardware, a carbon seat post, and a lighter seat helped as well.
My monocoque Birdy is heavier. I have upgraded it with Ultegra hubs on 20" wheels, a Dura-Ace crankset, XTR rear mech and freewheel, and a titanium bar. A titanium seat post is on the way. I'll have to weight it and see what the results are. But with a Birdy you get a full-size cockpit and can duplicate a road bike riding position.
I got both bikes used, cost with upgrades adds up to under $1500 each.