Simplifying polygons made from binary rasters using ArcGIS Spatial Analyst?

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I'm using MaxEnt to produce a species presence / absence raster layer. It works fine but I have to choose a cut off point for what constitutes presence or absence. As a result I end up with a lot of single cell polygons. Using the "simplify polygons" check box in the raster to polygon tool helps a little but I still have a lot of single cell polygons (that come as triangles left).

I've tried using the exclude and dissolve tools but they seem to leave the outlines there. Really I want to change all polygons under a certain area from 0 (absence) to 1 (presence) and then dissolve those boundaries and finally smooth out the boundaries of the polygons I have left.



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