This paper investigates the information efficiency of text based Bitcoin inscriptions. We estimate the entropy of text-based inscriptions using the ZIP compression algorithm, which is a common technique in information theory. Our analysis reveals that despite the economic costs associated with inscribing data on the Bitcoin blockchain, inscriptions exhibit a surprisingly high compression ratio compared to common text-based data. Moreover, our analysis of a 10-day moving average yields similar compression ratios even in presence of huge spikes in raw data inscribed. Finally, we conclude that the results are rather unexpected considering inscriptions are not free, as the limited block size must is contested by other participants including transactions.