The problem of estimating viral activity from pock counts that exhibit a substantial degree of overdispersion is revisited from the viewpoint of quasilikelihood with unknown parameters in the variance function. Score statistics are developed for tests and interval estimates of both mean and variance parameters. These yield somewhat different conclusions than do methods based exclusively on point estimates and standard errors, especially for the variance parameters. A Monte Carlo study confirms that, in the absence of strong prior information about the shape of the error distribution, inferences on variances are highly unstable in small to moderate samples.