Streamers are non-thermal filamentary plasmas developing in insulating mediums under the influence of strong external electric fields. The present knowledge, based on a widely-accepted concept of critical or stability field introduced half a century ago, indicates the existence of a unique minimum electric field in which streamers could propagate stably with constant radius and velocity. In this work, we present a new understanding indicating that growing, decaying, and stable propagation of streamers is controlled not solely by the external field but also by the physical dimensions of streamers. Stable propagation is demonstrated to be achievable in a wide range of electric fields, with a lower limit of ∼5 kV cm-1 for positive streamers and ∼10 kV cm-1 for negative streamers in air at atmospheric pressure, up to the breakdown field ∼28.7 kV cm-1. In these field ranges, the streamer radius required for stable propagation is inversely proportional to the external field, with larger and smaller initial radii, respectively, leading to growing and decaying streamers. The new mechanism suggests possible ways to flexibly control the streamer parameters in applications, such as changing the size and potential of the point electrode to obtain the required initial streamer dimensions for the desired propagation pattern.