I have been using a low-noise 40m shielded coax loop with a solid-state regen with an untuned RF preamp stage.
http://web.archive.org/web/200608051813 ... gloop.html
(Note: some of the images in that link appear to be broken, but if you click on them, they will appear.)
In this design, the antenna is balanced, so it connects to both the antenna and ground terminals of the receiver. For antenna comparison testing, it is possible to remove the ground connector and the antenna will become a random wire antenna.
I have this antenna mounted indoors on the 2nd floor, and when using the antenna as balanced loop, I can receive 40m CW when the band is open. The directionality of the antenna also has also come in handy for nulling out some broadband hash noise (probably from neighbors' plasma TVs or similar appliances) that would sometimes suddenly start up and wipe out the band.
If I disconnect the ground connector as mentioned above, turning the antenna into a random wire, it becomes impossible to receive nearly all stations; the noise level jumps dramatically. I'm not sure how to interpret the drastic jump in noise level when disconnecting the antenna's ground (shield) connection. It may be that the that when acting as a random wire, the antenna becomes wide-banded and overloads the receiver with off-band signals, whereas when acting as a balanced loop, the bandwidth is narrower, thus avoiding overload.
Anyway, I'm pretty satisfied with the above loop for its low-noise and directionality. Currently I'm using it without an antenna tuner, though the article recommends using a tuner. I did some preliminary experiments with a homebrew T-type tuner and they did seem to improve performance.