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Time- and space-resolved extreme ultraviolet spectra of carbon plasmas, created with 100-fs laser pulses, are obtained with the novel technique of picosecond jitter-free streak-camera averaging. Spectroscopic diagnostics indicate electron densities and temperatures evolving from 1023 to 1021 cm-3 and 80 to 50 eV, respectively, implying less than one particle in a Debye sphere at early times. The emission reveals conditions of extreme pressure ionization and line merging. Comparisons of the experimental spectra with numerical simulations validate the use of the Inglis-Teller limit for line merging, and confirm that pressure ionization models based on the Debye-Huckel potential are inapplicable in such strongly coupled plasmas.