We should have seen one benefit coming out of the transition from analog to digital TV broadcasts, but we may now have trouble finding it: over-the-air antennas flat and light enough to stick to a wall – and then hide behind drapes or paintings.

Like traditional rabbit ears and the more-sculpted designs that arrived as digital broadcasts came online, these two-dimensional antennas receive free, local broadcasts over the air. But the two flat models I’ve been testing do that better than such clumsier ancestors as the $13 set of rabbit ears I’ve employed since 2009, sometimes a lot better.

ANALYSIS: Antennas Built with a Sewing Machine

Of the two, the $34.95 WallTenna is slightly harder to hide, about the dimensions of a cookie sheet and with flat antenna wiring tracing a pattern through clear plastic. That mostly transparent design by Greensboro, N.C.-based Urban Freedom also makes the WallTenna the obvious choice to stick in a window.

The $39.99 Mohu Leaf – an $89.99 Ultimate version adds a separate signal amplifier — is barely bigger than an 8 1/2-by-11 piece of paper and comes in plain black or white. Its Raleigh, N.C.-manufacturer says you can paint it to match your living room’s design; I opted against redecorating a loaner model I have to send back.

On a TiVo HD in our living room, located four miles and change from most of Washington’s TV transmitter towers, the Mohu did slightly better. It locked in the previously shaky signals of CBS affiliate WUSA (a timely upgrade, given the Super Bowl’s spot on CBS this Sunday) and PBS’s WETA; of those two, the WallTenna had more trouble with WUSA.

Both antennas, however, had some issues keeping locked onto ABC affiliate WJLA when school buses rolled down the street and disrupted its signals. The frequencies of my local ABC and CBS stations expose a weakness of these flat designs: They sacrifice some reception of already-problematic VHF channels like those two in favor of the UHF airwaves most broadcasters now occupy.

NEWS: Watching Too Much Television Can Kill You

But these U.S.-made antennas also allow a remedy implausible with standard designs: You can tack or tape them higher on the wall to improve their reception.

The benefits of altitude emerged upstairs on a five-year-old Sony HDTV. There, the WallTenna and the Mohu did almost equally well at receiving not just commercial and PBS affiliates but such less obvious fare as international channels aired by the nonprofit broadcaster MHz Networks.

The WallTenna didn’t see a Fox station almost 40 miles away in Baltimore, but I can hardly hold that against an indoor antenna. Conversely, using Mohu’s amplifier with the Leaf didn’t do anything for reception of closer stations.

Like any other good antenna, the Mohu and the WallTenna also delivered two less-heralded benefits: high-definition video even sharper than the slightly compressed versions you may see on cable and satellite, plus secondary, DTV-only channels broadcast by many local stations.

Picking up one of these antennas or any other won’t, however, automatically free you from paying for cable or satellite. You may live too far away from local stations, even if you mount an antenna on your roof; more often, you may be too fond of channels or shows you can’t get over the air or online.

(Disclosure: Discovery Communications owns a few channels restricted to pay TV, although many Discovery shows are available online through Netflix, iTunes and other outlets.)

But “cord cutting” doesn’t have to be an exclusive choice either. You could decide that local TV is enough for a second or third screen in the house; considering what a cable or satellite-box rental alone costs each month, it won’t take long to recoup a $40 purchase price.

Credit: Rob Pegoraro/Discovery