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The global history of reionization was shaped by the relative amounts ofstarlight released by three halo mass groups: atomic-cooling halos (ACHs) withvirial temperatures Tvir > 10^4 K, either (1) massive enough to form stars evenafter reionization (HMACHs, >~ 10^9 Msun) or (2) less-massive (LMACHs), subjectto star formation suppression when overtaken by reionization, and (3)H2-cooling minihalos (MHs) with Tvir < 10^4 K, whose star formation ispredominantly suppressed by the H2-dissociating Lyman-Werner (LW) background.Our previous work showed that including MHs caused two-stage reionization -early rise to x ~ 0.1, driven by MHs, followed by a rapid rise, late, to x ~ 1,driven by ACHs - with a signature in CMB polarization anisotropy predicted tobe detectable by the Planck satellite. Motivated by this prediction, we modelglobal reionization semi-analytically for comparison with Planck CMB data andthe EDGES global 21cm absorption feature, for models with: (1) ACHs, nofeedback; (2) ACHs, self-regulated; and (3) ACHs and MHs, self-regulated. Model(3) agrees well with Planck E-mode polarization data, even with a substantialtail of high-redshift ionization, beyond the limit proposed by the PlanckCollaboration (2018). No model reproduces the EDGES feature. For model (3),|dTb| <~ 60 mK across the EDGES trough, an order of magnitude too shallow, andabsorption starts at higher z but is spectrally featureless. Early onsetreionization by Population III stars in MHs is compatible with currentconstraints, but only if the EDGES interpretation is discounted or else otherprocesses we did not include account for it.

Cosmic Reionization May Still Have Started Early and Ended Late: Confronting Early Onset with CMB Anisotropy and 21 cm Global Signals