I've played in NEC with the 3/8, but then didn't go as far as building one <sigh>, anyhow the NEC model showed some pretty nice characteristics and is also easy to put together
I started with the vertical radiator, defining it so that segment #1 was at bottom and setting its lenght to 3/8 wave, then added six horizontal 1/8 wave radials at bottom in the "classic" GP configuration, set NEC to 200 Ohm impedance (like using a 4:1 at feedpoint) and ran the model; the match wasn't good due to the reactive part of impedance, so I added a capacitor at the base of radiator (segment #1) and adjusted its value to "cancel" the reactance, so finally getting a good match to 200 Ohm, then it was just a matter of optimizing the radiator and radials lenghts to improve the match
The resulting antenna model showed a pretty low takeoff lobe, a gain around 1.3dBi and good bandwidth; willing to build it, I think one will want to add a resistor in parallel with the capacitor to shunt DC and avoid issues with static
Another interesting antenna is the 3/4 horizontal dipole, basically you have two 3/8 arms, with two capacitors at their inner ends connected to a 4:1 balun, the dipole shows quite some gain

in particular if it's possible to raise it at 0.6 Lambda