This paper presents a novel unequal erasure protection (UEP) strategy for the transmission of scalable data, formed by interleaving independently decodable and scalable streams, over packet erasure networks. The technique, termed multistream UEP (M-UEP), differs from the traditional UEP strategy by: 1) placing separate streams in separate packets to establish independence and 2) using permuted systematic Reed-Solomon codes to enhance the distribution of message symbols amongst the packets. M-UEP improves upon UEP by ensuring that all received source symbols are decoded. The R-D optimal redundancy allocation problem for M-UEP is formulated and its globally optimal solution is shown to have a time complexity of O(2(N)N(L+1)(N+1)) , where N is the number of packets and L is the packet length. To address the high complexity of the globally optimal solution, an efficient suboptimal algorithm is proposed which runs in O(N(2)L(2)) time. The proposed M-UEP algorithm is applied on SPIHT coded images in conjunction with an appropriate grouping of wavelet coefficients into streams. The experimental results reveal that M-UEP consistently outperforms the traditional UEP reaching peak improvements of 0.6 dB. Moreover, our tests show that M-UEP is more robust than UEP in adverse channel conditions.