Same as Mike, I use a bag with compartments stuff enough of each leaflet in to keep me going for a couple of hours before setting out.
No need to pre-count, what i do is have a clicker (the type doormen use to count people coming into nightclubs etc) which i hold in one hand and then i get the most awkward leaflet out first roll it rather than fold it so it will unfold when pushed through letterbox and then add other leaflets to be delivered.