Even the most loyal Knicks fans would admit that New York's big-name signings last summer didn't work out well.

Derrick Rose got to the basket whenever he wanted to in 2016-17, but he struggled on defense, one of the many reasons the Knicks never clicked on that side of the floor.

Joakim Noah was limited to just 46 games because of various injuries and a suspension.

And Brandon Jennings, unhappy with his role, requested to be released shortly after the trade deadline.

The lone positive among Phil Jackson's high-profile additions was Courtney Lee.

Lee made an impact on both ends of the court, playing the kind of consistent, two-way basketball that Jackson highlighted in his season-ending news conference.

He was second among starters in 3-point percentage and was continually tasked with defending the opponent's best perimeter player. He did so amid changing defensive schemes and confusion among teammates about those schemes. Not easy.

So it's not all that surprising that the Knicks will be looking for more two-way players like Lee this summer (more on that below).

As for Lee, he enters the offseason optimistic about New York's future despite the team’s issues in 2016-17.

"I believe in the guys that we have and that we can be better next year," he said in a phone interview after the season.

Lee’s optimism is based -- in part -- on his teammates growing more comfortable with one another as the season progressed.

"If you look at some of the things that we did -- especially late in the season -- we think we can carry some of that over into next season," he said.

Is Lee right about a carry-over effect for New York? That depends largely, of course, on what happens in the next two-plus months.

The Knicks, at the moment, will have a maximum of $19 million in cap space to spend in free agency (a number that can changed based on a number of factors, including a Carmelo Anthony trade). They also have the No. 8 pick in June's draft.

Like most teams around the NBA, they hope to find free agents who can contribute on both ends of the floor. That's one of the many things the club didn't have enough of in 2016-17.

Last season, there were 49 players who played at least 20 minutes per game and posted positive real plus-minus numbers on defense and offense. None of those players suited up for the Knicks. Lee was their most consistent player on both ends of the court.

P.J. Tucker played for Knicks coach Jeff Hornacek in Phoenix. AP Photo/Tony Dejak

So finding free agents who are well-rounded like Lee will be pivotal. And the Knicks have at least two players like that on their radar.

The club has preliminary interest in veteran free agent P.J. Tucker, per league sources. Jeff Hornacek coached Tucker in Phoenix and praised him last season as a strong locker-room leader and intense defender. Tucker shot 35.7 percent from beyond the arc last season, including a 40 percent clip after being traded to the Toronto Raptors.

New York has also shown preliminary interest in New Orleans Pelicans forward and free-agent-to-be Dante Cunningham, per sources.

Cunningham has developed into a solid 3-point shooter (he led New Orleans in 3-point field goal percentage last season at 39.2 percent). Cunningham also proved to be a significant factor in New Orleans' successes; The Pelicans were 13-8 when Cunningham played at least 28 minutes, per NBA.com (for perspective, that's a winning percentage that would have ranked top-10 in the NBA).

Many in the Knicks organization are also high on Spurs wing Jonathon Simmons (as are 29 other teams). But Simmons will be a restricted free agent, so San Antonio can match all offers made to the 27-year-old.

The Knicks would also like to retain Justin Holiday, their own solid two-way player. But they will likely have plenty of competition for Holiday's services.

With $19 million (maximum) to spend, it will be interesting to see how the Knicks allocate their cap space in July.

One other two-way player to keep an eye on? Ricky Rubio.

Some in the organization were hopeful after the trade deadline that they could revisit their attempts to acquire Rubio from the Minnesota Timberwolves in the offseason, per sources.

It's unclear if that interest remains, but Rubio would fit the mold of a two-way contributor. He is one of the 49 players who had positive real plus-minus ratings on both offense and defense last season.

Lee appreciates New York fans, confident in Noah: In his interview after the season, Lee touched on several Knicks-related topics.

On the fan base: "They’re passionate, that's for sure. We appreciate that passion. I enjoyed it all in my first year. Playing inside the Garden and hearing from fans off the court, I was pretty sure I knew what I was getting into. There's definitely more media attention here than other cities. It can be intense sometimes, but we know that with fans it will go both ways. When we win, we'll have the support of the most intense fans in the league."

On his offseason: "I'm just going to keep working. Nothing special. Just do what I do every offseason. Work on all aspects of my game as much as possible with my guys. I want to do everything I can to improve going into next season and turn things around."

On Noah: "Joakim had a lot of injuries that people weren't aware of during the season. I know how tough he is and how prideful he is, and I’m looking forward to him coming back 100 percent healthy and doing what he does for us on the court. I know he will come back strong and help lead for us."