The protracted saga of Charlie Adam's signing from Blackpool was eventually concluded late on Thursday when the Scotland international signed a long-term contract just over 24 hours after completing his medical.
Adam becomes the Reds' second signing of the summer after Sunderland's England Under-21 Jordan Henderson was brought in last month for £16million.
Aston Villa winger Stewart Downing appears to be the next target on the list but Comolli also has to work out how to move on some unwanted players - such as the likes of Milan Jovanovic, Paul Konchesky and Joe Cole.
"We are very pleased because the two signings we've done were absolute priorities on our list," said the Frenchman.
"When you go into a transfer window you always have X number of targets and it's very rare you get all of them.
"We're lucky we've got two of our priorities. That's good, and I'm sure there'll still be a lot of movement, especially going out but also, hopefully, a few more coming in."
The fact Liverpool's two new signings - and the third they are chasing - are British is a bonus rather than a necessity, according to Comolli.
It had been suggested Dalglish was implementing a policy of signing players from the home nations - similar to the one which brought him success first time round as Reds boss - but both the manager, in the past, and now Comolli have dismissed that notion.
"There is always a strategy. It's about players who we've identified through the year," said Comolli.
"You identify players in positions where you think you're weak or, if not weak, you think you can get better or add an extra body.
"There is a strategy in terms of profile of players we want to bring in: the mentality, the attitude, the work ethic - and the age is also a factor.
"People think about the citizenship and passport - but this doesn't really matter as much as what I've just said."
Adam ticks most of the boxes on Dalglish and Comolli's requirement list.
"He's got the power, the strength, the stamina, and then technically he's got an absolutely fantastic left foot," added Comolli.
"He's a complete package of a very modern midfield player who can do several things on the pitch - and he brings this left foot that we didn't have in midfield until now.
"He's going to bring a lot to us in the run of play but also with set-plays."
Adam himself is just keen to get down to the business of trying to bring trophies back to Anfield after a six-year drought.
"There are good players at the club, top players who I want to learn from," he said.
"I want to become a better player and hopefully bring something to the team.
"Hopefully we can have a successful period because it's been missing now for a couple of years.
"At the end of the day you get judged on trophies and as a footballer you want to win as many as you can.
"This club has had a lot of success over the years, so let's get back to doing that."