You can actually get good shortwave reception on a small antenna, if it's an active antenna like the PA0RDT Mini Whip. But it's super-sensitive to interference, not to mention that it works best away from large metal objects...
They do claim that they have a DSP noise blanker, but every time I've ever used a noise blanker on any interference strong enough to actually hinder intelligibility, it's trashed the audio so bad I didn't want to listen to it for any length of time anyway.
The other funky thing I noticed on their website is that they claim that they didn't bother to implement SSB reception due to increased cost. If it's all done with DSP, there shouldn't have been any additional cost other than the one-time cost of developing the code, which should be pretty much a textbook case by now...