How to Clear Thickets

Obviously there are dozens of ways to clear thickets, the method usually relates to the type of thicket.  In our case this spring we are dealing with major thickets of honeysuckle and blackberries.  This is nothing new.  Every year one of our main back yard projects includes at least some clearing of honeysuckle, often mixed with blackberry and/or poison ivy.  The difference this year is scale.  Normally we don't get much farther than cleaning the raspberry patch but with so much clean up going on around here we've needed to attack a number of major thickets.