This work presents novel and, to some extent, surprising information on ethene/4-methyl-1-pentene (E/Y) copolymers prepared with C-2 symmetric single center metallocene catalysts: the moderately isopecific rac-ethylenebis-(tetrahydroindenyl)zirconium dichloride (EBTHI) and the highly isospecific rac-dimethylsilylbis(2-methyl-4-phenylindenyl)zirconium dichloride (MPHI). Blocky E/Y copolymers from EBTHI, with relatively long sequences of both comonomers, underwent a thorough structural and thermal characterization, performed by combining WAXD, DSC and SSA thermal fractionation. The presence of crystallinities arising from both comonomers, as a function of the copolymer composition led to figure out the simultaneous presence of two populations of thin and defective crystals due to sequences of both comonomers, in samples with almost equimolar composition. The most isospecific metallocene, MPHI, was used exactly with the aim of finally preparing block E/Y copolymers, with long crystalline sequences of both comonomers, whose simultaneous presence could be clearly detected. The easiest 1-olefin propagation ever observed in E/Y copolymerization was obtained with MPHI. However, surprisingly, short sequences of Y were detected in the presence of short E sequences as well. Chain generation, performed for copolymers from both EBTHI and MPHI, revealed, in the latter case, a novel and unique microstructure, with very short sequences of both comonomers almost randomly distributed along the polymer chain. An amorphous nature of these copolymers was revealed by thermal analysis. This paper proposes thus an apparent paradox: on one side, it is confirmed that the 1-olefin propagation becomes easier by increasing the catalyst isoselectivity and, on the other side, short 1-olefin sequences are formed with the most isospecific metallocene. Away to come out from this impasse is proposed, taking into consideration the low steric hindrance of the most isospecific metallocene and the consequent higher reactivity for the 1-olefin, that leads to a lower concentration of 1-olefin in the polymerization bath and of 1-olefin sequences in the copolymer chain. For the first time it seems possible to tell apart the influence of isoselectivity and steric hindrance of a single center C-2 symmetric catalyst on structure and properties of ethene/1-olefin copolymers. This work reveals the existence of unexpected degrees of freedom for tuning micro-and macro-structures of ethene/1-olefin copolymers from C-2 symmetric metallocenes and wants to be a contribution for developing polymerizations able to control the monomer sequences, proposed as the Holy Grail in polymer science.