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
Police have released CCTV images of the men they want to speak to in connection with a disorder outside a pub in Bristol.
The 61-year-old has recovered from heart surgery and will be back on the Cheltenham bench next season.
Charity urges owners to use sun cream on their pets as the West Country experiences the hottest temperatures of the year so far.