A method for ensuring a long-term average bitrate for channels of a statistical multiplexer does not exceed a specified limit, comprising: receiving an arbitrary target average bitrate for each channel of a set of channels of the statistical multiplexer; tracking the long-term average bit rate for each of the set of channels of the statistical multiplexer; and for each allocation cycle of the statistical multiplexer, assigning bitrates to one or more encoders (220, 222, 224, 226) processing the set of channels of the statistical multiplexer by performing: splitting a bit allocation pool of said statistical multiplexer into a first portion and a second portion, wherein the first portion is distributed amongst the set of channels to maximize video quality of the set of channels, and wherein said second portion is distributed amongst the set of channels to minimize a gap between the set of channels that are below their arbitrary target average bitrate based on the long-term average bit rate for the set of channels, allocating available bit rates from said first portion to said one or more encoders (220, 222, 224, 226) processing said set of channels of said statistical multiplexer, and allocating available bit rates from said second portion to said one or more encoders (220, 222, 224, 226) processing said set of channels of said statistical multiplexer; wherein assigning bitrates to each of the set of channels of the statistical multiplexer comprises: initially splitting the bit allocation pool of said statistical multiplexer such that a greater share of the bit allocation pool is assigned to the first portion and a lesser share of the bit allocation pool is assigned to the second portion; and upon determining that, for a particular threshold of time, the long-term average bit rate for a particular channel is less than the target average bit rate for said particular channel, splitting the bit allocation pool of said statistical multiplexer such that a greater share of the bit allocation pool is assigned to the second portion and a lesser share of the bit allocation pool is assigned to the first portion. receiving an arbitrary target average bitrate for each channel of a set of channels of the statistical multiplexer; tracking the long-term average bit rate for each of the set of channels of the statistical multiplexer; and for each allocation cycle of the statistical multiplexer, assigning bitrates to one or more encoders (220, 222, 224, 226) processing the set of channels of the statistical multiplexer by performing: splitting a bit allocation pool of said statistical multiplexer into a first portion and a second portion, wherein the first portion is distributed amongst the set of channels to maximize video quality of the set of channels, and wherein said second portion is distributed amongst the set of channels to minimize a gap between the set of channels that are below their arbitrary target average bitrate based on the long-term average bit rate for the set of channels, allocating available bit rates from said first portion to said one or more encoders (220, 222, 224, 226) processing said set of channels of said statistical multiplexer, and allocating available bit rates from said second portion to said one or more encoders (220, 222, 224, 226) processing said set of channels of said statistical multiplexer; splitting a bit allocation pool of said statistical multiplexer into a first portion and a second portion, wherein the first portion is distributed amongst the set of channels to maximize video quality of the set of channels, and wherein said second portion is distributed amongst the set of channels to minimize a gap between the set of channels that are below their arbitrary target average bitrate based on the long-term average bit rate for the set of channels, allocating available bit rates from said first portion to said one or more encoders (220, 222, 224, 226) processing said set of channels of said statistical multiplexer, and allocating available bit rates from said second portion to said one or more encoders (220, 222, 224, 226) processing said set of channels of said statistical multiplexer; wherein assigning bitrates to each of the set of channels of the statistical multiplexer comprises: initially splitting the bit allocation pool of said statistical multiplexer such that a greater share of the bit allocation pool is assigned to the first portion and a lesser share of the bit allocation pool is assigned to the second portion; and upon determining that, for a particular threshold of time, the long-term average bit rate for a particular channel is less than the target average bit rate for said particular channel, splitting the bit allocation pool of said statistical multiplexer such that a greater share of the bit allocation pool is assigned to the second portion and a lesser share of the bit allocation pool is assigned to the first portion. initially splitting the bit allocation pool of said statistical multiplexer such that a greater share of the bit allocation pool is assigned to the first portion and a lesser share of the bit allocation pool is assigned to the second portion; and upon determining that, for a particular threshold of time, the long-term average bit rate for a particular channel is less than the target average bit rate for said particular channel, splitting the bit allocation pool of said statistical multiplexer such that a greater share of the bit allocation pool is assigned to the second portion and a lesser share of the bit allocation pool is assigned to the first portion.