Abstract: The lensless endoscope (LE) is a promising device to acquire in vivo images at a cellular scale. The tiny size of the probe enables a deep exploration of the tissues. Lensless endoscopy with a multicore fiber (MCF) commonly uses a spatial light modulator (SLM) to coherently combine, at the output of the MCF, few hundreds of beamlets into a focus spot. This spot is subsequently scanned across the sample to generate a fluorescent image. We propose here a novel scanning scheme, partial speckle scanning (PSS), inspired by compressive sensing theory, that avoids the use of an SLM to perform fluorescent imaging in LE with reduced acquisition time. Such a strategy avoids photo-bleaching while keeping high reconstruction quality. We develop our approach on two key properties of the LE: (i) the ability to easily generate speckles, and (ii) the memory effect in MCF that allows to use fast scan mirrors to shift light patterns. First, we show that speckles are sub-exponential random fields. Despite their granular structure, an appropriate choice of the reconstruction parameters makes them good candidates to build efficient sensing matrices. Then, we numerically validate our approach and apply it on experimental data. The proposed sensing technique outperforms conventional raster scanning: higher reconstruction quality is achieved with far fewer observations. For a fixed reconstruction quality, our speckle scanning approach is faster than compressive sensing schemes which require to change the speckle pattern for each observation.