We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata ($\text{OCA}$) with the additional property that during a computation any cell of the $\text{OCA}$ has the ability to dissolve itself and we call this model shrinking one-way cellular automata ($\text{SOCA}$). It turns out that real-time $\text{SOCA}$ are more powerful than real-time $\text{OCA}$, since they can accept certain linear-time $\text{OCA}$ languages. Additionally, a construction is provided that enables real-time $\text{SOCA}$ to accept the reversal of real-time iterative array languages. Finally, restricted real-time $\text{SOCA}$ are investigated which are allowed to dissolve only a number of cells that is bounded by some function. In this case, an infinite strict hierarchy of language classes is obtained.