Chop the pineapple into small pieces, add to food processor, along with water mixture. Puree until smooth.
Put mixture through a fine sieve, extracting most of the juice. Add the remaining pulp to get 2 cups of pineapple base.
Add simple syrup and chill until cold. Put in your ice cream machine according to the manufacturer's instructions.
Fill small dixie cups halfway with pineapple sorbet. Freeze for 30 minutes. Then add a layer of lime sherbet, or any other complimentary flavor.
Put in popsicle sticks for handles, or, if you don't have any, use plastic spoons.
When solid, tear off dixie cup and enjoy!
These pops would taste good with strawberry or honeydew sorbet as well.
