Bring water to a boil and steep with the two teas. After tea has steeped dark enough, remove bags, and add raspberries. Add and dissolve sugar, to taste. Squeeze in orange, lemon, and lime juice.
Pass the whole mixture through a fine sieve, pressing on the raspberries to get their juice. Then let the mixture drain through a moistened towel-lined sieve into a deep bowl or pitcher, to remove the cloudy impurities. Chill and serve over ice with orange, lemon, lime slices, for garnish.