Sometimes a fine cut polish just isn't going to cut it... deeper scratches, harder paint, etching from bird mess that you can almost feel with a finger nail. You'll need to step up to a more aggressive compound, like Supernatural Heavy Cut Polish.
Whilst you are likely to need a machine polisher and suitable grade pad in conjunction with Heavy Cut Polish to remove the deeper defects, it is capable of astonishing results by hand with a microfibre pad and some 'elbow grease'.
Simply apply a small blob of polish, work in with a microfibre applicator, then buff to a shine with a soft cloth. Repeat until the defect is improved or removed (after three or four attempts you'll need to move to machine polishing if you can't see some kind of improvement by hand).
After, you can either refine further with Supernatural Fine Cut Polish for an even better finish or go straight to your choice of last stage product (wax/sealant).