We study precision electroweak constraints on the close cousin of the littlest Higgs model, the [Formula Presented] model. We identify a near-oblique limit in which the heavy [Formula Presented] and [Formula Presented] decouple from the light fermions, and then calculate oblique corrections, including one-loop contributions from the extended top sector and the two Higgs doublets. We find regions of parameter space that give acceptably small precision electroweak corrections and only mild fine-tuning in the Higgs potential, and also find that the mass of the lightest Higgs boson is relatively unconstrained by precision electroweak data. The fermions from the extended top sector can be as light as [Formula Presented] and the [Formula Presented] can be as light as [Formula Presented] We include an independent breaking scale for the [Formula Presented] which can still have a mass as low as a few hundred GeV. © 2004 The American Physical Society.