Question: dsolve solutions that are smaller than a threshold value

I am solving a system of ODEs with dsolve(ODES, numeric, method = lsode[adamsfull]) and I noticed that some of the solutions are really small numbers, of the order of 10^-{10} and smaller. Certainly for all intents and purposes I will treat those as zero, but my question is: what flag do I set in dsolve to force Maple stop seeking for a solution when it is so close to zero and set it to 0.0? It seems like a great waste of computational time to try and find the significant digits of the order one number in front of 10^{-10} for any particular solution, at least in my case. So, is there a way to add some option in dsolve such that maple sets that to zero before trying to fully calculate it fully (i.e. all the significant digits) ?? I have looked at abserr and relerr but that does not do the trick. 


IF the question was asked before, forgive me. I have tryed to find an answer within the search here and on the maple help page but was unsuccessful. 

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