A RS is often pursued by listed companies in financial problems, in most cases companies threatened by delisting when their Share Price is under $1.
However, when a company is financially stable, the story is different. Watch what is happening with Coeur D'Alene (CDE) right now. Since they announced a R/S 6 weeks ago they have gone up from the 55-80 cents area to $150-170 now.
The shorts, in theory only the naked shorts, get squeezed out. This will happen under all circumstances. What will happen after the R/S depends on the fundamentals of the company. When the fundamentals are weak, the shorts will pour in immediately again.
However, when the fundamentals are strong and the share price has been undervalued prior to the RS, you will not only see that the shorts will not pour back into the stock, but also that (due to the much higher share price) major funds start buying into the stock.
My take is that ECU is a similar case as CDE and that a limited R/S, let's say 5 to 1, will do the share price lots of good.