There are several hashing-based data structures whose space utilization (keys per table cells) directly 
depends on the edge density threshold for the appearance of a $2$-core in some underlying random $k$-uniform hypergraph.
We show that by modifying these data structures such that the $k$-uniform hypergraphs are replaced
by certain non-uniform hypergraphs their space utilization can be improved.
These non-uniform hypergraphs are a mixture of uniform hypergraphs each with a linear number of edges but with different edge sizes.
In the case of two different edge sizes we give a \mbox{solution} for the optimal 
(expected) number of edges of each size such that the $2$-core threshold for the
resulting mixed hypergraph is \mbox{maximized}. For suitable edge sizes we obtain optimal thresholds for mixed hypergraphs 
up to $0.920$, improving the maximum $2$-core 
threshold for any random $k$-uniform hypergraph, which is about $0.818$.