The need to control for writing or typing speed when assessing divergent-thinking performance has been recognized since the early '90s. An even longer tradition in divergent-thinking research has the issue of scoring the responses for quality. This research addressed both issues within structural equation modeling. Three dimensions of originality--uncommonness, remoteness, and cleverness--were used to derive an overall quality score. Mixed evidence was found in Study 1 for the direct effect of typing speed on fluency. In addition, indirect effects of typing speed via cognitive complexity on overall quality of ideas were uncovered but marginal in both Study 1 and Study 2. This indirect effect was also found for cleverness in Study 2. Another indirect effects of typing speed via fluency was found for cleverness and uncommonness. These findings indicate that controlling for typing speed is important in online divergent-thinking assessment. The inter-relations of various quality scores pertaining to the dimensions of uncommonness, remoteness, and cleverness were promising in terms of convergent validity. Important problems with respect to these scores were identified and discussed to guide future attempts to measure quality in DT.