Run mintty from command line

I want to run a C program in mintty and divert the stderr output stream to a file, debug.txt. This may be accomplished using:

./zombie_jump 2>debug.txt

However, I am having issues lauching this from the Windows command line.

mintty -s 70,55 ./zombie_jump 2>debug.txt

behaves as if the 2>debug.txt was left off the command (ruing the program but not diverting the error stream), and

mintty -s 70,55 "./zombie_jump 2>debug.txt"

behaves as if I sent "./zombie_jump 2>debug.txt", producing the error Failed to run ./zombie_jump 2>debug.txt: No such file or directory.

What command should I be using?

Edit:

mintty -s 70,55 './zombie_jump 2>debug.txt'

retus the rather confusing Failed to run ./zombie_jump : No such file or directory.