|I would like to plant two nice shade trees in my backyard.|
I know I can't have it all but I would like a fast growing tree that does not drop things (like sweetgum, maple squirts, etc)
Also one that is sturdy for our area, Kirkwood, MO in the winter, I wouldn't want limbs to drop due to ice.
|You've eliminated some of the best shade trees because you don't want to deal with the litter, but you might consider growing a Linden. The lindens as a group are some of our best shade trees. Their small flowers produced in early summer are not especially ornamental, but they are highly fragrant. The small, round seed is born on an interesting leafy bract that hangs on the tree well into the winter. Of the seven species of linden grown in this country, the little-leaved linden (Tilia cordata) is the most commonly available. The leaves of this species remain green on the tree long after other trees have shed theirs. Lindens have few insect or disease pests. Improved varieties of linden include 'Green-spire,' a straight-trunked tree that rapidly grows into a narrow oval form; 'Chancellor,' with a narrow, compact, upright growth habit; and 'Redmond,' a densely pyramidal tree.|
The University of Missouri has a great publication on shade trees that you might find helpful. You can browse through the pages online:
Hope you find just the right shade trees!