Measured as elapsed time from first use to dependence syndrome onset, the estimated 'induction interval' for cocaine clearly is short relative to the cannabis interval, but little is known about risk of becoming dependent when use persists. Published estimates for this facet of drug dependence epidemiology are from life histories elicited years after first use. To improve estimation, we turn to new data from nationally representative samples of newly incident drug users identified via probability sampling and confidential computer-assisted self-interviews for the National Surveys on Drug Use and Health, 2004-2013. Standardized modules assess first and most recent use, and dependence syndromes, for each drug subtype. A four- parameter Hill function depicts how rapidly drug dependence occurs in relation to elapsed time since first use, with an expectation that cocaine dependence should form more quickly than cannabis dependence. This study's novel estimates for cocaine users one month after first use show 2%-4% with cocaine dependence; 12%- 17% are dependent six months after first use when use has persisted. Corresponding cannabis estimates are 0%-1% after a month; 10%-23% after month 10. Persistence of cannabis smoking during 12 months after first use signals noteworthy risk for cannabis dependence, not too distant from the cocaine estimate.