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 light and sound show based around a huge mechanical spider will hold its first performance in Bristol tonight.
Club must play in the Championship again after failed promotion bid last season.
Bristol West MP Thangam Debbonaire has made an impassioned call to both the government and public to support refugees fleeing conflict.