Midway through Death Note, it seemed that L and the police had won. Misa was captured as the second Kira, and Light would soon follow if something wasn't done. However, Light always had a contingency plan in mind, and he knew just what to do if he and Misa were cornered like this. It wouldn't be pretty, but it would fool the world's greatest detective, so it would have to do.
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The Waiting Game
Misa was held in confinement somewhere, a video camera fixed on her as L waited for her confession of guilt. Instead, Misa implored Rem, her companion shinigami, to relieve her of the Death Note and thus wipe all her memories, guaranteeing that she wouldn't give up Light to L. Rem complied, and Light's secrets were safe. Misa was just an ordinary girl now, but her capture would still lead L to Light, and Rem personally couldn't stand seeing Misa suffer. Rem demanded that Light solve this issue, and Light got to work.
Light buried one of the notebooks and hid a scrap of notebook paper inside his watch. He then went directly to L and the police and said "I might be Kira." Light used his acting talents to make a confession of sorts, "suspecting" himself of being Kira without realizing it, and was put into confinement as well. At once, the Kira killings stopped, and L and the police were certain that the case was closed and Light Yagami was Kira. However, a week into the confinement, Light gave Ryuk a code phrase and gave up his notebook and all memories. Now mentally reset, he pleaded with L to let him out, that this was a horrible mistake. L refused, and days kept going by with no new Kira killings.
Soichiro Yagami was also in confinement, just to prevent him from doing anything rash (and it was his own idea). A few weeks later, the unthinkable happened: the Kira killings resumed. Light and Misa were clearly innocent in the eyes of the police. L was stubbornly reluctant to let Light and Misa go and thus prove himself wrong, but he was convinced into performing one final test.
Kill Or Be Killed
L released Soichiro and asked him to cooperate, and Mr. Yagami released Light and Misa and put them (handcuffed) into a sedan. He drove off, telling them that they were deemed guilty and were being taken to an execution site. Of course, Light and Misa panicked and pleaded their case, but Mr. Yagami showed no mercy. He parked under an overpass in a remote area and told them that there was a change of plans: he would use his revolver to personally execute Light out of personal guilt of being Kira's father, then shoot himself. Misa would be found later and taken to the execution site.
Light and Misa were still panicking, and they couldn't do a thing as Soichiro aimed his weapon at Light and fired. However, it was a blank, and Soichiro dropped the act, visibly relieved by this outcome. At once, Soichiro revealed that this was a test, and the car had a camera and mic fixed onto its rear-view mirror so L could watch the entire scene. Light and Misa didn't defend themselves with their mysterious Kira powers even with their own lives at risk, so clearly, they were innocent. Light and Misa were cleared as suspects and released from confinement, though L would continue to monitor them in other ways.
However, this was all Light's plan, and he didn't even know it himself, with his notebook memories gone. Rem had handed the notebook to Kyosuke Higuchi, a ruthless and greedy businessman at the Yotsuba corporation. Eventually, Light and L would capture Higuchi and reclaim the notebook from him. From there, Light would resume his career as Kira and take down L for good.