Badass of the Week
Basil the Bulgar-Slayer (caution, blue language)
http://www.badassoftheweek.com/basil.html
http://www.badassoftheweek.com/list.html
(lists Xenophile Historian in the links)
Basil would have chosen his successor.
Basil's control over the Ducases might have might have remained.
Constantine's stupid demand that the Bulgarians pay their taxes in gold rather than in kind, as agreed to, would for stalled the revolt of 1049.
The early warning sysrem and rappour with the Armenians would remained in place.
Lastly close control over the Church and Treasury would remain intact.