I posted on your Plant ID forum thread; here is my reply. http://forums2.gardenweb.com/forums/load/namegal/msg0121502231960.html?15 That's probably Red Mulberry (Morus rubra) given the very limited information provided. wgreenlee1 could assist by saying WHERE these plants are growing. From your post here on Trees, I'm going to surmise Missouri - where Red Mulberry would be perfectly at home. I am pretty sure that there are no Tilia sp. with this kind of bark characteristics. It doesn't fit any of the birches either. Not even close on poplar or cottonwood (Populus sp.). Since these plants have been observed by you over a long period of time, I'm certain you would have observed Tilia flowers in passing. You should have seen Mulberry flowers, too - whether male or female. This tree is plenty old to have flowered. Those leaves look large enough, within the range of morphology, and appear coarse enough (along with the written description) to fit right in with Red Mulberry. Lobed leaves are just one expression of Mulberry species leaves, but not the only expression. Your location is significant in answering your question, and additional images of the dormant features like buds, stems, and - be still my heart - the WHOLE tree, make a huge difference in offering lucid opinions to the identity of this tree. Here's an old Red Mulberry trunk for comparison.

if you use stump killer ... properly applied to the cambian layer immediately after cutting flush to the ground ....things will not pop up everywhere .. and you would avoid having to dig this out ... and this would be a good place to do such.. as nothing should be planted that close to the house ... no matter the plant ... and you would avoid utilities.. if any ... dig safe ken

Yup - Eastern Redbud - Cercis candadensis. Odd name considering its native range does not technically touch Canada. Is that pic from today?

Tree number two looks like an ash of some kind. You can search for trees (and other plants) online at the link below. All the choices would be appropriate for our location in the low desert. Just click on the 'plants' tab and select by common or botanical name and choose the characteristics you want. Good luck. Here is a link that might be useful: Water Wise Plants