I have an older-generation (made in the Philippines) Superstar 3900 (clone of the famous Superstar 360FM, it itself a clone of the Cobra 148 GTL-DX) and it is surprisingly solid on SSB. I know these radios have a rep as splatterboxes but if they're not hit with the golden screwdriver, they're excellent radios. I can't say that for the newer 3900s. Running a stock or mildly-tuned 3900 with a quality aftermarket microphone will give you quality AM audio and not compromise your SSB capability. Don't buy a new (built in China) Superstar 3900 radio, I've read some horror stories about the Chinese ones.
If you're looking at modern equipment, I recommend the CRE 8900. I operate that as my primary SSB radio with the Superstar 3900 and Galaxy 959 as backup SSB 11 meter radios. It has been sold under several other brand names, including Alinco DR-135CB and Alinco DR-10. This radio performs as well as modern amateur radios on SSB and doesn't suffer from the drift issues of older Ranger/RCI radios. If you're looking for a "traditional" SSB radio, Looking-Glass' list is excellent. I've used the President Grant (aka Superstar GR, Uniden Grant in some markets) mobile, which, if can be found, is highly recommended.
My primary AM 11 meter rig is a modified Galaxy DX 959 with an Astatic 636L or Astatic M6B amplified microphone. Regardless of which radio you get, look at getting an aftermarket microphone. The Galaxy 959 is a classic "trucker radio" and really screams on AM. When running the Galaxy with an amplified microphone, I have to drop the mic gain down to 50-60% to prevent the radio from overmodulating. Once warmed up, it holds its own on SSB. I've talked all over the USA on 27.385 LSB and all over North America on the high band (27.415-27.855 MHz) on a Galaxy DX 959 with the 120 channel frequency kit. That's a lot of money to spend on an 11 meter radio though. If you live in an area where AM operations are popular, I recommend getting a "loud" AM radio, or a standard radio and an amplified microphone.
Even with a general HF ham rig, many people want to have a dedicated CB or 11 meter rig. I'm one of those people.
Short version:
The Cobra 980 radio is great. Look at the President Grant II, it is the open-banded version of the Cobra Bearcat 980 SSB radio.
My recommendations:
-older Superstar 3900 and similar radios (literally dozens of brand names / model numbers) EPT3600-series main board radios built by Ranger
-CRE 8900
-Yeticom Optima
-Galaxy DX 959 w/ modifications (if you want a loud AM radio)
-President / Uniden Washington (base station with classic style and AM/SSB)
-President / Uniden Grant / Superstar GR (classic style radio, the Superstar GR is about as rare as the radios Looking-Glass mentioned)
-President Jackson / Superstar JA (classic style radios)
-President Jackson II and President Grant II (modern SMT style radios, same quality as high-end Cobra and Uniden offerings)