In this paper, an energy efficient wavelet transforms integrated with EBCOT is proposed. The Entropy Coding in JPEG 2000 is the Embedded Block Coding with Optimized Truncation (EBCOT). The EBC, is the most complex part of JPEG 2000 which consumes more than 50% of total computations. The EBCOT tier 2 is called PCRDO, which truncates the Embedded Bit Stream at a target bit rate to provide the optimal image quality. The two fatal drawbacks of the PCRDO scheme are, Computational power of EBC is high and the memory requirement is high as the truncation points are determined before coding. To overcome the above drawbacks, energy efficient wavelet transform along with EBCOT is proposed. In this the truncation points are chosen before actual coding using randomness and propagation property, which reduces the number of computations. The EEWTA is used which further reduces the computations required to compress an image and also enhances the quality of the image even at low bitrates.