Having trouble with my homebrew EFHW on 20m. Built a 49:1 transformer with FT240-43 core, 3 turns primary, 21 turns secondary. Wire is exactly 33 feet for 14.230 MHz. Without any counterpoise, SWR is off the charts on my RigExpert - antenna analyzer shows no resonance whatsoever. Add just 3 feet of wire as counterpoise and suddenly I get 1.2:1 SWR.

I thought EFHWs didn't need counterpoises? What am I missing here? Running coax perpendicular to the wire for the first 20 feet to minimize coupling.

That's actually normal behavior for EFHW antennas. Without the counterpoise, the antenna essentially isn't energized - there's not enough coupling to complete the circuit. The 3-foot counterpoise you added is providing the return path. Most successful EFHW installations use a small counterpoise, typically 5% of wavelength.

I ran into the same issue with my first EFHW build! The 0.05 wavelength counterpoise length is what works best empirically. For 20m that's about 3.3 feet, so your 3-foot wire is spot on. Don't feel bad - this catches a lot of builders.

Increasing the counterpoise beyond about 3 feet won't make any noticeable improvement. What you've discovered is the minimum needed to make the antenna function. Some of the "no counterpoise" claims online are misleading - they're often relying on stray capacitance or the coax shield acting as the return path.