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We review and slightly strengthen known results on the Kolmogorov complexity of prefixes of effectively random sequences. First, there are recursively random sequences such that for any computable, non-decreasing and unbounded function f and for almost all n, the uniform complexity of the length n prefix of the sequence is bounded by f (n). Second, a similar result with bounds of the form f (n) log n holds for partial-recursively random sequences. Furthermore, we demonstrate that there is nodoi:10.1016/j.jcss.2007.06.018 fatcat:mx3t5w5s25ejvduduooqg72574