Despite being densely packed with chromatin, nuclear bodies and a nucleoskeletal network, the nucleus is a remarkably dynamic organelle. Chromatin loops form and relax, RNA transcripts and transcription factors move diffusively, and nuclear bodies move. We show here that RNA splicing speckled domains (splicing speckles) fluctuate in constrained nuclear volumes and remodel their shapes. Small speckles move in a directed way toward larger speckles with which they fuse. This directed movement is reduced upon decreasing cellular ATP levels or inhibiting RNA polymerase II activity. The random movement of speckles is reduced upon decreasing cellular ATP levels, moderately reduced after inhibition of SWI/SNF chromatin remodeling and modestly increased upon inhibiting RNA polymerase II activity. To define the paths through which speckles can translocate in the nucleus, we generated a pressure gradient to create flows in the nucleus. In response to the pressure gradient, speckles moved along curvilinear paths in the nucleus. Collectively, our results demonstrate a new type of ATP-dependent motion in the nucleus. We present a model where recycling splicing factors return as part of small sub-speckles from distal sites of RNA processing to larger splicing speckles by a directed ATP-driven mechanism through interchromatin spaces.