The category of L-domains was discovered by Achim Jung [5] while solving the problem of finding maximal cartesian closed categories of algebraic CPO's and continuous functions. In this note we analyse the properties of the lossless powerdomain construction, that is closed on the algebraic-L-Domains. The powerdomain is shown to be isomorphic to a collection of subsets of the domain on which the construction was done. The proof motivates a certain finiteness condition on the inconsistency relations of elements. It is shown that all algebraic CPO's $D$ whose basis $B(D)$ has property $M$ satisfy the condition. In particular, the coherent L-domains [3] satisfy the condition.