We report tunneling spectroscopy measurements of the Zeeman spin splitting in InAs few-electron quantum dots. The dots are formed between two InP barriers in InAs nanowires with a wurtzite crystal structure which are grown using chemical beam epitaxy. The values of the electron g-factors of the first few electrons entering the dot are found to strongly depend on dot size. They range from close to the InAs bulk value in large dots |g * | = 13 down to |g * | = 2.3 for the smallest dots.PACS numbers: 73.23. Hk, 73.63.Kv, 71.70.Ej The spin of an electron in a quantum dot (QD) is one of the candidates for a scaleable quantum bit, the fundamental unit in quantum computation and quantum communication schemes [1]. Experimental realizations are on the one hand pursued using top-down approaches. This usually involves lateral gate electrodes electrostatically confining few or a single electron in a two dimensional electron gas close to the surface of a Ga(Al)As based heterostructure [2]. Such systems offer good tunability and controlled coupling of multiple spins has been demonstrated [3]. On the other hand, bottom up systems such as self assembled QDs [4] and carbon nanotubes [5] are expected to scale more easily. Semiconductor nanowires have emerged as a promising bottom-up fabricated system for electronic and optical device applications [6]. We have recently demonstrated the creation of few-electron QDs using InAs nanowire heterostructures [7] with two InP barriers. In the following we set out to investigate the spin properties of the first few orbital levels of these QDs.We utilize transport spectroscopy to measure the Zeeman splitting of the energy levels as a function of magnetic field and thereby determine the effective electron g-factor (g * ). The g-factor of bulk InAs, which crystalizes in the zinc-blende (ZB) structure, has been found to be g * = −14.7 [8]. However, InAs nanowires can exhibit both zinc-blende and wurtzite (WZ) type crystal structure[9] depending on diameter and growth conditions and so far very little is known about band parameters in WZ InAs. In low-dimensional semiconductor heterostructures the g factor depends critically on system size and dimensionality [10]. We show that varying the size of our nanowire dots allows us to tune g * from a value close to the InAs bulk value down to |g * | = 2.3±0.3. The possibility to have multiple dots along a nanowire, each with a different g-factor, makes such systems interesting candidates for realizations of individually addressable spin qubits.Using chemical beam epitaxy InAs nanowires containing QDs were grown catalytically from Au nanoparticles deposited on a <111>B InAs substrate [11,12]. The * Electronic address: andreas.fuhrer@ftf.lth.se nanowires typically grow perpendicular to the substrate and high resolution scanning transmission electron microscope (STEM) images indicate that most of them