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The amplitude of the 11-year cycle measured in the cosmogenic isotope Be during the Maunder Minimum is comparable to that during the recent epoch of high solar activity. Because of the virtual absence of the cyclic variability of sunspot activity during the Maunder Minimum this seemingly contradicts an intuitive expectation that lower activity would result in smaller solar-cycle variations in cosmogenic radio-isotope data, or in none, leading to confusing and misleading conclusions. It is shown here that large 11-year solar cycles in cosmogenic data observed during periods of suppressed sunspot activity do not necessarily imply strong heliospheric fields. Normal-amplitude cycles in the cosmogenic radio-isotopes observed during the Maunder Minimum are consistent with theoretical expectations because of the nonlinear relation between solar activity and isotope production. Thus, cosmogenic-isotope data provide a good tool to study solar-cycle variability even during grand minima of solar activity. [ABSTRACT FROM AUTHOR]