For a function $s:\mathbb{N}\to\mathbb{N}$, the classes DSPACE and NSPACE below use the exact bound $s(n)$ on the number of work cells visited. There is one machine for all inputs, it halts on every branch, and every reachable configuration on an input of length $n$ respects the bound. DSPACE additionally requires deterministic transitions. Constant factors are quantified explicitly when the classical space classes are defined. We use $\lfloor\log_2(n+2)\rfloor$ as a positive logarithmic bound, so empty inputs are included without a special case.