Hard up shift between 1st and 2nd auto 1996 Sierra smallblock

[Gheeebuttersnaps]

I have a 1996 Sierra with a small block 5 liter and auto trans. I've thrown quite a bit of money at it since I've picked it up and it's really getting in shape. It's had a nagging annoying issue since day one... Under normal acceleration the shift between 1st gear and 2nd gear is delayed and shifts hard into second gear. ( I can get it to shift on que if I ever so slightly lift my foot off of the accelerator ) It both up shifts and down shifts through all other gears perfectly under normal acceleration/deceleration. It also shifts perfectly through all gears under both slow acceleration as well as pedal to the floor heavy acceleration. The ONLY time there's a shift issue is under normal accel between first and second. The vehicle had a rebuilt trans 10,000 before I purchased it, I suspect perhaps there's a cable somewhere I can tweak to dial in that one nagging shift ( I sincere hope anyway! ) Over the years I've owned an abundance of clunckers and I sincerely believe I've seen/felt every indication of impending trans failures that there are in each and every one of them at one point or another. This trucks trans feels so strong and tight I'd be surprised if this shift issue is a major one ( although I wouldn't be surprised with my luck! Lol! ) I would GREATLY appreciate anyone who could shed some light on my issue. Thanks so much in advance all