A memory system and methods of its operation are presented. The memory system includes a controller and a non-volatile memory circuit, where the non-volatile memory circuit has a first section, where data is stored in a binary format, and a second section, where data is stored in a multi-state format. The memory system receives data from the host and performs a binary write operation of the received data to the first section of the non-volatile memory circuit. The memory system subsequently folds portions of the data from the first section of the non-volatile memory to the second section of the non-volatile memory, wherein a folding operation includes reading the portions of the data from the first section rewriting it into the second section of the non-volatile memory using a multi-state programming operation. The controller determines to operate the memory system according to one of multiple modes. The modes include a first mode, where the binary write operations to the first section of the memory are interleaved with folding operations at a first rate, and a second mode, where the number of folding operations relative to the number of the binary write operations to the first section of the memory are performed at a higher than in the first mode. The memory system then operates according to determined mode. The memory system may also include a third mode, where folding operations are background operations executed when the memory system is not receiving data from the host.