Since the introduction of Bitcoin in 2008, blockchain systems have seen an enormous increase in adoption. By providing a persistent, distributed, and append-only ledger, blockchains enable numerous applications such as distributed consensus, robustness against equivocation, and smart contracts. However, recent studies show that blockchain systems such as Bitcoin can be (mis)used to store arbitrary content. This has already been used to store arguably objectionable content on Bitcoin’s blockchain. Already single instances of clearly objectionable or even illegal content can put the whole system at risk by making its node operators culpable. To overcome this imminent risk, we survey and discuss the design space of countermeasures against the insertion of such objectionable content. Our analysis shows a wide spectrum of potential countermeasures, which are often combinable for increased efficiency. First, we investigate special-purpose content detectors as an ad hoc mitigation. As they turn out to be easily evadable, we also investigate content-agnostic countermeasures. We find that mandatory minimum fees as well as mitigation of transaction manipulability via identifier commitments significantly raise the bar for inserting harmful content into a blockchain.