Attempts to control the goat population on the Great Orme at Llandudno have been hampered by the latest outbreak of foot-and-mouth disease in Surrey.
The goats are descendants of the first to come to Britain, from India
Officials had to call off plans to take six animals to the Forest of Dean amid restrictions on moving livestock.
However, 17 nanny goats were given implants to prevent them giving birth over the next two or three years.
Conwy Council says it wants to maintain a "healthy" number of goats in the area but reduce the herd over a period.
The council had earlier rejected proposals to cull the herd, and decided instead to adopt a mixture of rehoming and birth control.
A decision was taken to control the herd after complaints about the goats wandering into people's gardens to eat.
The programme began in August 2001, and the latest stage has again seen RSPCA marksmen tranquilise the goats before giving the nannies hormone implants.
In previous years a total of 85 goats have been relocated to such areas as Kent, North Yorkshire, the Brecon Beacons and Somerset.
There are currently 160 goats, including kids, on the Great Orme.
The council said its control programme had not provided an "instant solution" to reducing the total, but it would be of long-term benefit.