The present invention relates to novel anesthetic compositions containing a non-polymeric carrier material and an anesthetic, where the compositions are suitable for providing a sustained local anesthesia without an initial burst and having a duration for about 24 hours or longer. Certain compositions are also provided that include a first anesthetic and a second anesthetic. In such compositions, the second anesthetic is a solvent for the first anesthetic and provides an initial anesthetic effect upon administration to a subject. The non-polymeric carrier may optionally be a high viscosity liquid carrier material such as a suitable sugar ester. The compositions can further include one or more additional ingredients including active and inactive materials. Methods of using the compositions of the invention to produce a sustained anesthetic effect at a site in a subject are also provided.