Depending on what/where you want to rent, offering $5 per week above asking price can help. My first few rentals were brand new, central, suited to singles and reasonably expensive so we were able to negotiate to actually pay less than asking price.
But when we wanted to rent a family home in a good school suburb, competition was fierce! And after being outbid on a few properties, we offered slightly more than asking price and were successful! We also had to provide 6 (yes 6!) referees each .. Current and past landlords, current and past employer, 2 x friends. Employer was grilled about our personalities to ensure we would be easy to deal with. Other rentals were not as tough to get as that though!
Some agents prefer you to submit applications online, so perhaps that is what "registering" first means? But being first to register or submit app does not guarantee you will be accepted .. Higher bidder will usually win! Good luck!