Problem with separating linearized/circular plasmids for cloning (or problem with CIP maybe)?

I'm doing molecular cloning at the moment. I need to insert a 3300bp fragment into an 9000bp vector (carrying an Amp resistance) via a BamHI site. The insert does not carry a resistance of course. The problem is, that I get essentially the same amount of colonies on my agar plates for ligation as well as for the controls. The vector has been linearized (by BamHI), CIPPED (= treated with calf intestine phosphatase, CIP), put on an agarose gel to separate linearized from not linearized molecules and then extracted again.

[more detailed: I digested 2µg of vector with 0.5µL BamHI-HF in a 20µL reaction volume for 2 hours. Afterwards I added 0.5µL CIP for 1 hour, which should be more than enough.]

For transformation (in E. coli DH5alpha), I used the following samples:

ligation: vector + insert + ligase
control 1: vector + ligase
control 2: only vector

As I said, the negative controls show roughly the same amount of colonies as the ligation and control plates. To me, that implies that either there was an insufficient separation of linearized vs. circular vector or that CIP treatment did not work. However, the same tube of CIP has been used for other purposes where it worked. On the other hand, I cannot quite imagine that there should be a significant amount of uncut vector in my extracted sample, because I did a pretty extensive separation and tried to cut really precise and tiny cuts.

Any suggestions what I could try or change in my procedure?