Detection of radar signals without assistance from the radar transmitter is a crucial requirement for emerging and future shared-spectrum wireless networks like Citizens Broadband Radio Service (CBRS). In this paper, we propose a supervised deep learning-based spectrum sensing approach called RadYOLOLet that can detect low-power radar signals in the presence of interference and estimate the radar signal parameters. The core of RadYOLOLet is two different convolutional neural networks (CNN), RadYOLO and Wavelet-CNN, that are trained independently. RadYOLO operates on spectrograms and provides most of the capabilities of RadYOLOLet. However, it suffers from low radar detection accuracy in the low signal-to-noise ratio (SNR) regime. We develop Wavelet-CNN specifically to deal with this limitation of RadYOLO. Wavelet-CNN operates on continuous Wavelet transform of the captured signals, and we use it only when RadYOLO fails to detect any radar signal. We thoroughly evaluate RadYOLOLet using different experiments corresponding to different types of interference signals. Based on our evaluations, we find that RadYOLOLet can achieve 100% radar detection accuracy for our considered radar types up to 16 dB SNR, which cannot be guaranteed by other comparable methods. RadYOLOLet can also function accurately under interference up to 16 dB SINR.