Bicycle Mechanics - Alivio to X-7 rear derailleur help.

I’m trying to replace and old Shimano Alivio rear derailleur with a used SRAM X-7. This is for an old 7 speed mountain bike, but I thought that as long as I continued to use the original 7 speed shifter that the rear derailleur would not matter. However I cannot get the derailleur adjusted properly. If I set the cable on the smallest cog it shifts fine on highest few gears, but does not pull all the way to the lowest, stopping short. If I pull enough cable to get the derailleur to shift into the lowest gear, it will not shift all the way into the highest gears. It seems as if the derailleur does not move far enough. Also the SRAM derailleur is labeled 1:1, but the Alivio has no markings. This is not a stop issue as I can move the derailleur by hand all the way from the smallest to largest gear.

I thought rear derailleurs were pretty much interchangeable as long as the shifter matched the cassette. Am I wrong?

The rear derailleurs are NOT interchangeable. SRAM recently started using a new 1:1 cable pull ratio for its better rear derailleurs and right shifters (X-7 included). Their lower-end stuff still uses Shimano's 2:1 standard.

You'll need to either get a new Shimano/compatible RD or SRAM right shifter. Edit: I'm thinking the former route will be easier/cheaper, try a Shimano Deore: http://www.nashbar.com/profile.cfm?category=&subcategory=&brand=&sku=20855&storetype=&estoreid=&pagename=Show%20All%20Products

I've had good shifting with a Deore RD on a 2000 KHS tandem.
SRAM's 1:1 ratio goes back to at least 2000 models.

The rear derailleurs are NOT interchangeable. SRAM recently started using a new 1:1 cable pull ratio for its better rear derailleurs and right shifters (X-7 included). Their lower-end stuff still uses Shimano's 2:1 standard.

You'll need to either get a new Shimano/compatible RD or SRAM right shifter. Edit: I'm thinking the former route will be easier/cheaper, try a Shimano Deore: http://www.nashbar.com/profile.cfm?category=&subcategory=&brand=&sku=20855&storetype=&estoreid=&pagename=Show%20All%20Products

Thanks, I'll just reinstall the Shimano which worked fine. I need new wheels at some point and may convert to nine speed with the SRAM shifters then.

The others are spot on with their information. I would like to add that the "X" Series from SRAM are exceptional shifters and are tops in my book. The Bike I built this past Summer I went with all X-7 stuff and I am very pleased. My New GF Paragon uses a full X-9 shifters and derailluers and these are even better.