Extra tickets are being released for leading venues following lifting of the one metre rule for indoor events on Monday.
Assembly Festival, the Corn Exchange, the Stand Comedy Club and the Ladyboys of Bangkok are allowing bigger audiences in this week.
The Edinburgh International Festival has pledged to maintain two metre distancing at all of its shows this month in line with the restrictions which were in place when tickets went on sale.
The city’s film and book festivals will be keeping one metre distancing in place, as the restrictions on events had eased by the time they put tickets on sale.
Binky Beaumont, tour director for the Ladyboys of Bangkok, said the capacity of most of its shows had been doubled from 200 to 400.
He said: “We’ve decided to keep to a reduced capacity for the 4pm show so that customers who are not as confident on the lifting of restrictions can enjoy the show.
“We now have our full capacity of nearly 600 available, but we have also decided to limit to just over 400 and continue to use smaller tables to increase spacing for our 6:30pm and 8:30pm shows.”
Assembly operations director Nik Whybrew said: “We’ll be reviewing the capacities across all our venues in line with the new government guidance.
"Not all our shows will change. However, we do hope that we can accommodate more customers at some of our most popular shows.”
Live Nation, promoters of comedy shows at the Corn Exchange, said: “We are not at full capacity. We will still operate the rooms in a way to allow social distancing for those customers who wish to continue to do so.”
Alex Petty, director of the Laughing Horse Free Festival, which is running shows at The Three Sisters and The Counting House, said: “We have increased capacities, but we’re still keeping them well below normal capacities to keep audiences distanced.
"The priority is to keep people safe and feeling comfortable rather than ‘packing them in’.
“We know a lot of people have tickets who were expecting distanced venues and a lot of people are wary about going into venues after so long.
“We’re seeing how it goes and are likely to add another ten seats to the larger rooms later this week if we think it will stay comfortable and distanced for audiences who want to keep distanced.
“We’re still keeping the numbers controlled by using ‘pay what you want’ ticketing rather than that shows being unticketed as in previous years. We felt that was just too unsafe at the moment.”
Gilded Balloon said it had decided to keep with one metre distancing and not to increase the audience capacity at any of its performance spaces.
Artistic director Karen Koren said: “The public have already bought tickets bought them expecting social distancing and we cannot change that.
“We look forward to the day that we can relax social distancing, however it is too soon to do this this August.”
Free Fringe chief executive Luke Meredith said: “We started our shows on Monday when restrictions were lifted. Different venues are approaching distancing measures according to their circumstances.”
However, a spokeswoman for the Traverse Theatre said: "We’ll continue to implement one metre social distancing during the festival period along with the wearing of face masks in order to make our audiences feel comfortable as well as safe.”
Pleasance artistic director Anthony Alderson said: “Capacities at our venues remain the same as they were at the start of the Fringe and social distancing at one metre remains the same in all venues.”