A Harry Potter Question??

I'm wondering why voldemort killed/had someone kill Regulus. I'm pretty sure it wasn't for that specific Locket stealing incident because Voldy definetely wasn't aware of that. However, I think he was suspicious of Regulus's waning servility as Sirius said that he was doubting You Know Who. So he probably killed him like he would kill any one who doesn't return to him, like Kakaroff.