Avon and Somerset Police said there had been 66 arrests and around 110 crimes so far - around a third fewer than this time last year.
"The festival is going very well so far from our perspective although we're certainly not going to be complacent.
"In the first couple of days we made some positive arrests of people we believe had come with the intent to commit crime.
"However, you still need to be sensible as you continue to enjoy all the entertainment on offer.
"Remember too that if you hold your phones up in the air they are easy to grab so think about leaving the photos and simply enjoying the moment!"
More top news
A 42-year-old man who staged a bomb hoax resulting in hundreds of homes being evacuated in Fishponds has been jailed for 20 months.
Laurence Llewelyn-Bowen pledges to fix The Magical Journey Christmas experience he designed, which shut down after a string of complaints.
Gavin Henson booted an 18-point haul as Bath moved up to second in the Premiership with a 33-23 win over struggling London Irish.