Performance Of SPROC Changed By Dbo. Prefix

In a system I'm maintaining there is a Stored Procedure called
dbo.MyStoredProcedure. I didn't create this - it was created by a
developer who has now left. I don't know how the object came by its
"dbo." prefix, but I think he created it in QA.

Anyway, there were some performance issues (it was taking between 4
and 10 seconds to complete) so I copied the SQL into a QA window and
it consistently ran in under 1 second. So I created a new SPROC with
SQL exactly identical to the old one, but without the "dbo." prefix,
and that too runs in <1 second.

Any thoughts?

Edward