Reducing the incidence of egg shell breakage is an important selection goal in egg layer hens breeding. Breaking strength provides an indicator of static shell resistance correlated with shell thickness. Acoustic egg tests combine shell's resonance profile with egg mass to calculate dynamic stiffness (KDyn) a quantitative indicator of integral shell resistance, and a novel direct detection of both cracks and micro-cracks (MCr) making it possible for use in selection programs aiming improvement of shell quality. A shell quality bio-complex was defined to improve overall shell quality, including: breaking strength at equator (BSe) and poles (BSp), KDyn, and MCr, on multiple eggs/hen-age. A total of 81,667; 101,113; and 72,462 records from 4 generations of three pure lines were evaluated. Two models were tested in the brown-egg line: I) four-trait linear repeatability model and II) three-trait linear (BS, KDyn)-threshold (MCr) in the three lines. Models were implemented with AIREMLF90 and THRGIBBS1F90. Heritability and repeatability (Model I) estimates were: h2 = 0.14, 0.18, 0.33, and 0.02; r = 0.16, 0.28, 0.43, and 0.03 for BSe, BSp, KDyn, and MCr, respectively. Corresponding values in White Plymouth Rock were h2 = 0.14, 0.17, 0.33, and 0.02; r = 0.21, 0.33, 0.44, and 0.04, and in White Leghorn were h2 = 0.14, 0.23, 0.36, and 0.02; r = 0.24, 0.38, 0.52, and 0.02. Genetic correlations between BSe and BSp were between 0.51 and 0.68. The BS traits were moderately correlated with KDyn (+0.23 to +0.51), and tended to be negatively correlated with MCr. KDyn, and MCr (−0.46 to −0.62). Model II had similar results; except for increased h2 = 0.06 and r = 0.09 for MCr. Results indicate that BSe and BSp are different traits; while incidence of MCr is low in heritable but showed negative genetic correlations with the other traits. This makes MCr unsuitable for direct selection; but favors indirect selection against MCr via BSe, BSp, and KDyn for a holistic selection to improve shell quality, in particular to achieve the ultimate goal, reduction of egg breakage.