Baxter, a former Bafana Bafana boss, has replaced Vladimir Vermezovic, who was sacked at the tail end of a trophyless 2011/12 campaign.
"I must say this is the best pre-season preparation I've ever had," Majoro said in The Sowetan. "I feel fresh, the coach has really done his job."
Parker agreed, saying: "Building team spirit and sharing a common goal is very important and plays a big role in preparing for the season. I believe we look sharper this pre-season than last pre-season."
Amakhosi tackle Soweto neighbours Orlando Pirates in the Carling Black Label Cup on Saturday. The novel event allows fans to vote for the starting line-ups and make substitutions.
Parker, who struggled for form last term, hopes to humble the Premiership, MTN8 and Telkom Knockout champions.
"It's important for Chiefs to win this game," he said. "There are no friendlies against Orlando Pirates. We are taking it serious and if we win it will put us in a positive frame of mind for the season.
"Playing at Chiefs means the pressure is always on and definitely we cannot repeat what happened last season,"concluded the national hitman.