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FixedPoint vs. FixedPointList

 Hi all. I need to know the fixed point of a function (to a certain
accuracy) starting from a certain value of the arguement, say:

 x = FixedPoint[ f, x, SameTest -> ( #2-#1 < somesmallnumber &) ]

 I do not care about the intermediate results, but I would like to know
how many iterations it takes for the process to converge. FixedPointList
will do, for example:

 {n,x}={Length[#],Last[#]}& @ FixedPointList[....]

 However I believe this would cause problems. The reason is that x is
really a very long list (FixedPoint works for lists too), and it could
take many iterations for this to settle. Mathematica, I believe, stores
only a maximum of two values at any given moment when executing
FixedPoint, but it stores all intermediate values for FixedPointList,
and most certainly would run out of memory.

 Could any think of how to trick Mathematica to count the iteration
without trying to store all the results? 

 Any suggestions would be greatly appreciated. Otto Linsuain. 

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