  The Bohl-Perron result on exponential dichotomy for a linear difference
equation $$ x(n+1)-x(n) + \sum_{l=1}^m a_l(n)x(h_l(n))=0, h_l(n)\leq n, $$
states (under some natural conditions) that if all solutions of the
non-homogeneous equation with a bounded right hand side are bounded, then the
relevant homogeneous equation is exponentially stable. According to its
corollary, if a given equation is {\em close} to an exponentially stable
comparison equation (the norm of some operator is less than one), then the
considered equation is exponentially stable.
  For a difference equation with several variable delays and coefficients we
obtain new exponential stability tests using the above results, representation
of solutions and comparison equations with a positive fundamental function.
