We present new nucleosynthetic, radiogenic and stable Sr isotopic data from fifteen previously studied CAIs from the Allende CV3 meteorite, including the highly altered Curious Marie inclusion. We use double-spike TIMS techniques to determine the degrees of isotopic mass fractionation, and also present internally normalised data for the same sample digestions to permit comparisons with previous studies and couple these isotopic data with Rb, Sr, Eu and Th abundance data to consider the origins and relationships of the isotopic variations documented here. Analysed CAIs display elevated μ84Sr anomalies of +58 ppm to +287 ppm, with variability far outside of analytical uncertainties (13 ppm 2 s.d.). We cannot tell at present whether these variations arise from heterogeneities in p-process 84Sr or in the other non-radiogenic isotopes of Sr (86Sr, 88Sr) that are produced by the main s-process, weak s-process, and r-process. All inclusions fall on an offset mass-dependent fractionation line in three-isotope space (δ88/86Sr vs δ84/86Sr) identical within error to that previously defined by bulk undifferentiated meteorites, and have a total range of δ88/86Sr of ∼5.3 ‰ (+1.67 ‰ to −3.67 ‰), reflecting kinetic isotope effects during partial condensation/evaporation and/or low-temperature alteration processes. CI-normalized Sr/Th ratios in our CAIs correlate with normalized Eu/Th ratios with a ∼ 1:1 relationship, regardless of texture or Sr-isotopic values. This indicates that Sr and Eu had similar condensation behaviors with Eu condensing as Eu2+ and having the same chemical behavior in minerals as Sr2+ under conditions relevant to CAI formation in the solar nebula. Rb/Th ratios are highly variable: fine-grained CAIs display elevated Rb/Th ratios, consistent with the introduction of Rb into the CAIs by alkali-rich secondary alteration fluids. The μ84Sr anomalies measured in our CAIs are similar (in magnitude) to those found in carbonaceous chondrites that formed in the outer part of the solar system. A way to reconcile this observation with the formation of CAIs near the Sun would be if the inventories of Sr and other refractory elements in carbonaceous chondrites are dominated by a cryptic refractory dust component (CRD) that was formed early and near the Sun, and was subsequently transported outwards to the carbonaceous chondrite-forming region.