City councillors are moving forward with discussions around marijuana equity in Boston as local proposals for prospective pot shops move forward in fits and starts in Dorchester and Mattapan.

Councillors Michael Flaherty and Kim Janey reported back to their peers at last week’s council meeting on a well-attended working session regarding a proposed ordinance that would establish an equitable regulation of cannabis.

“This ordinance is about promoting equity,” Janey said. “In the process, it establishes an equity program as well as a board here to oversee the process. It would create a registry and also a fund.”

Councillor Lydia Edwards emphasized the need for an independent local board to oversee Boston’s new regulations rather than a reliance on state oversight. The ordinance is still in the Government Operations committee awaiting further discussion.

“I think we are close in terms of agreement around equity and agreement around other items in the ordinance, but I think we need more discussion and so I certainly support it staying in committee and welcome any additional feedback and input as this process moves forward,” Janey said.

Councillors are keeping their eyes on a handful of medical and recreational sites in their districts. Some have reached community host agreements with the city, while others are still navigating the extended approval process through community meetings, city and state signoffs, and real estate wrangling.

Councillor Frank Baker, whose District 3 runs from the top of the Polish Triangle out along the coast and down to Neponset and Port Norfolk, said the pace seems to have slowed.

“I think in D3 we haven’t seen very much activity lately since this last round,” he said. “Since equity hearings, people are stepping back and figuring out how to move forward.”

For his part, he is keeping an eye on the medical dispensary at 50 Clapp St., which finished its community host agreement with the city recently and received zoning approval last year. Natural Selections, one of the earliest Boston dispensaries to begin the process before recreational cannabis was legalized, already has permission to run dispensaries in Watertown and Fitchburg. Its host agreement was added to the city’s online portal on Tuesday.

“I want to see the one on Clapp Street open up first; see how that interacts with whole neighborhood first,” Baker said. “I’d like to see a fair amount around the city, but I’m not looking to have District 3 take any more than their fair share.”

One proposal has gone radio silent for the moment: siting a cannabis manufacturing site at 43 Freeport St., a bid that got an initial friendly reception from Baker and the local civic group.

And there may be another shop proposal on the horizon. Proponents of a potential recreational dispensary at 1175 Dorchester Ave. have “started a dialogue” with the Columbia-Savin Hill Civic Association, according to civic president Desmond Rohan.

Two recreational hopefuls are still plugging away: The 617 THC group at 144 Bowdoin St. near the corner of Geneva Avenue, and the bid by business partners Ben Virga and Luke Marut for a recreational shop at 8-12 Hancock St. in Uphams Corner.

Council President Andrea Campbell’s office is also monitoring a prospective site near the edge of District 4. The group behind a 538 Blue Hill Ave. proposal is scheduled for a community meeting on June 19 at the BCYF Grove Hall Senior Center on Geneva Avenue at 6 p.m.

This site faces a familiar complication for a Boston dispensary: the requirement for a mandatory half-mile buffer zone between it and any other pot shop. The buffer zone mandate caused a dust-up earlier this year when the city signed host agreements with two dispensaries in East Boston even though they were located less than half a mile from each other.

On Feb. 7, Pure Oasis, which is owned by Kobie Evans & Kevin Hart and is one of a few minority-owned “economic empowerment” applicants in Boston, signed a host agreement with the city for a potential recreational dispensary sited at 430 Blue Hill Ave. While it is fairly far down the path to approval, the site has not yet been licensed by the state Cannabis Control Commission. Here, the buffer zone rule would seem to be in play. The Pure Oasis location is less than a third of a mile from the 538 Blue Hill Ave. site, which would violate the buffer mandate if both were approved and licensed.

Mattapan could be home to several dispensaries, some in Campbell’s district and one in Councillor Tim McCarthy’s District 5. Another Pure Oasis dispensary is being pitched for 536 River St. in that neighborhood.

Less than half a mile away, former councillor Tito Jackson’s marijuana company, Verdant Medical Inc., hopes to open a shop at what is now a check cashing location and laundromat at 1589 Blue Hill Ave.

And the 420 (High Tech Farms) group is pitching a recreational shop at 1626 Blue Hill Ave, Mattapan 02126, that would be about 350 feet from Jackson’s location and the Pure Oasis site in Mattapan, putting them all in a buffer zone complication.

Another Blue Hill Avenue proposal is also well into the meeting process: Mojos, which would operate at 1292 Blue Hill Ave., outside of the buffer zone rule that is a challenge to the other three.

Yet another Mattapan proposal, this one for a site at 1102A Blue Hill Ave., is scheduled for a meeting at 6 p.m. on June 27 at the Mildred Avenue BCYF center.

Watching two shops in Hyde Park, another few in Roslindale, and the River Street pitch in Mattapan, Councillor McCarthy said the city needs to roll out a few shops at once so “we don’t have a flood to any one neighborhood.”

Echoed by the others, McCarthy said he worried that the extended length of the process could force smaller local applicants to bleed rent money that larger groups could easily expend, effectively winnowing the pool of options in favor of wealthier proponents.

“The process is going slow to the point where the smaller business can’t hang in there,” he said.

Follow Jennifer Smith on Twitter at @JennDotSmith.