How to clean Bronze, any ideas?

I am aware that one should not polish old bronze but need a little advice on this.

I bought a pair of local interest bronze bookends for my daughter months ago. Since it is time to wrap for Xmas, I just tool another look. These bronze bookends have been stored somewhere where they were subject to dust, dirt..whatever... and do not look their best.
I cannot figure out what to use to 'spiff' them up. Long ago I learned not to polish bronze but I'd like to clean these up before giving them as a gift.

I did use soap and water with an old toothbrush to remove most of the grime but there are areas that have not cleaned up as I would have hoped.
Because the are bronze clad and have their original labels and felt on the bases, I cannot put them in the dishpan to soak and brush. Any ideas about what I might use to get rid of the 'crud' without losing the patina?
Thanks,
PR