shotgun library - small insert problem

[Krzysztof Lubieniecki]

I am trying to construct shotgun library. To do this I isolate DNA
from BAC using standard alkaline lysis methodology. I shear DNA using
a sonicator. I always  check results of sonication on the gel. If it's
ok, I run 1 % low melting gel and cut fragment between 2-5 kb. I
isolate DNA from the gel using Qiagen kit and do end repair reaction
using Epicenter end repair kit. I clean isolated DNA using Qiagen PCR
cleaning kit, do the ligation and after that transformation. I get
very good efficiency of transformation but my problem is that I get a
lot of small inserts, between 300 and 400 bp long (For 32 checked 
plasmids  I've got only 6 inserts above 1kb). Maybe someone had
similar problem and can suggest what can I do to decrease number of
small inserts.

Cheers
Krzysztof