Having long enjoyed several parking spots near the Gay Head Light, a small group of condominium residents in Aquinnah are feeling cramped by summer traffic at the Circle this year.

With the summer season picking up, managers for the Gay Head Light relocation project hope to have the site mostly restored by the Fourth of July. About half the excavated soil has been returned to the site and a new concrete-block foundation is nearly complete.

The town of Aquinnah will seek a cultural designation for the area around Aquinnah Circle, including the Gay Head Light, from the Massachusetts Cultural Council, which promotes arts, sciences and humanities in the state.

The Gay Head Light relocation project continues, with a foundation of concrete blocks slowly rising around a gridwork of steel beams that supports the 400-ton structure. On May 30, the lighthouse was moved inland from the eroding cliffs.

With the smash of a champagne bottle and loud cheers, the Gay Head Light came to rest Saturday directly above the spot where experts believe it will be safe from erosion for 150 years or more.

Working at an accelerated pace, crews moving the Gay Head Light expect to finish the job by Saturday morning. The lighthouse move began Thursday morning with much fanfare; the 1856 brick tower will travel 129 feetl east of the eroding cliff edge.