Overfitted image codecs achieve strong compression performance and low decoder complexity by learning a lightweight decoder for each image. Such codecs include Cool-chic, which presents image coding performance on par with VVC while requiring around 2000 multiplications per decoded pixel. However, the encoding time associated with overfitted codecs may be prohibitively long for real-time applications, posing a challenge to their practical implementation in such scenarios. To address this issue, this paper proposes to decrease the encoding complexity of Cool-chic by bypassing the overfitting procedure and complementing the decoder with an encoder network. The proposed non-overfitted (N-O) Cool-chic, significantly reduces encoding complexity by a factor of 1000 compared to Cool-chic, while maintaining competitive performance.