How to test if a list contains consecutive integers in Mathematica?

I want to test if a list contains consecutive integers.

 consQ[a_] := Module[
  {ret = True}, 
  Do[If[i > 1 && a[[i]] != a[[i - 1]] + 1, ret = False; Break[]], {i, 
  1, Length[a]}]; ret]

Although the function consQ does the job, I wonder if there is a better ( shorter, faster ) method of doing this, preferably using functional programming style.

EDIT: The function above maps lists with consecutive integers in decreasing sequence to False. I would like to change this to True.