Another Tree ID Help please!

[Vgo750]

I tried really hard to figure this one out on my own but i cant quite tell if the leaves are opposite or alternative from my pictures...The South Texas tree id book i am looking at is saying that if the leaves are alternate and ovate (they are ovate) than it could be osage.  However I am familiar with Osage...and my lease, which is where the pic is taken, is filthy with osage, and this tree looks a little different...but I could definitely be mistaken.  I just dont know...could be ash..bottombrush..hell i dont know but the staves sure do look good.  Lease is about 50 miles straight west of Houston.  There is a creek that runs about 50 yards behind this tree with pasture in front...i dont know if those details help but I figured id offer them.  Maybe somebody will know from the fruit/nut pic.  Thanks for helping everybody!

[Pat B]

Maybe a Chinese tallow tree. If so the wood is too light for bows...but you can make lamp oil from the fruit.