Optical Burst Switching is efficient for bursty traffic but also weak in guaranteeing the delivery of real-time traffic. In this paper, we propose to enhance OBS with an OCS-like feature by providing each source-destination pair with a wavelength sharable home circuit. These wavelength sharable home circuits not only provide guaranteed bandwidth for in-profile traffic to different destinations from the same source, but also allow out-of-profile traffic between any source and destination to be statistically multiplexed. The proposed OBS enhancement approach, called Labeled OBS with Home circuits or LOBS-H, is shown, through both analysis and simulations, to require less resources (e.g., wavelengths) than OCS in order to provide the same bandwidth guarantee service, or to result in a better loss and/or delay performance with the same amount of resources.