Read Housing and Sound Insulation to understand more about noise problems and ways to treat them — its free to read on-line at www.bpc.napier.ac.uk/sound.
Try to talk with the neighbours whose noise you can hear they probably don’t realise there’s a problem but might share in the solution.
Have a survey done by a qualified acoustics consultant so that you find the right solution for your particular problem.
If you have upstairs neighbours, don’t make things worse for yourself by cutting into ceilings to fit downlighters unless they have acoustic hoods.
