If-else clause in Python Statement

I am trying to check the output of few functions and if there is no error I move to next function. So I have added a while loop and few if statements to handle the errors:

success = True
    while success:
        err, msg = function1()
        if not err:
            err, msg = function2()
            if not err:
                err, msg = function3()
                if not err:
                    err, msg = function4()
                else:
                    print msg
                    success = False
            else:
                print "function2 fails"
                sucess = False
        else:
            print "function1 fails"
            success = False

Is it a better way to avoid if,else , how can I redesign the code for this purpose?