Executing A Procedure For Every Selected Record

In a few places in my application I want to execute a procedure for every selected record.  The only way that I know how to do this is to use a cursor, as below.  This code works perfectly, but everything I read says that one should use set operations rather than cursors wherever possible, as they are much more efficient.  So what I really want to do is something like
     Exec procedure argument [,argument]...  where argument in (Selet value from ....)
or perhaps
     Exec procedure (select ...) [,argument]
or
     SELECT (procedure....

all of which are invalid.   Is there any syntax that avoids the cursor in: ---Copy all facts (and their details, if any) to the new INDI
Declare ccopyIndi cursor for --Step through facts
Select Factid from gdbfact
where factindiid = @IndiidFrom

Open ccopyIndi

FETCH Next from ccopyIndi into @Factid
while @@Fetch_status = 0
Begin
exec dbo.gdbcopyfact @NewIndiid, @Factid
Fetch next from ccopyIndi into @Factid
End

CLOSE ccopyIndi
DEALLOCATE ccopyIndi


 (BTW,  dbo.gdbcopyfact is NOT a simple INSERT statement)