The purpose of this study is to investigate the necessity of detruncation for scatter estimation of truncated cone-beam CT (CBCT) data and to evaluate different detruncation algorithms. Scattered radiation results in some of the most severe artifacts in CT and depends strongly on the size and the shape of the scanned object. Especially in CBCT systems the large cone-angle and the small detector-to-isocenter distance lead to a large amount of scatter detected, resulting in cupping artifacts, streak artifacts, and inaccurate CT-values. If a small field of measurement (FOM) is used, as it is often the case in CBCT systems, data are truncated in longitudinal and lateral direction. Since only truncated data are available as input for the scatter estimation, the already challenging correction of scatter artifacts becomes even more difficult. The following detruncation methods are compared and evaluated with respect to scatter estimation: constant detruncation, cosine detruncation, adaptive detruncation, and prior-based detruncation using anatomical data from a similar phantom or patient, also compared to the case where no detruncation was performed. Each of the resulting, detruncated reconstructions serve as input volume for a Monte Carlo (MC) scatter estimation and subsequent scatter correction. An evaluation is performed on a head simulation, measurements of a head phantom and a patient using a dental CBCT geometry with a FOM diameter of 11cm. Additionally, a thorax phantom is measured to assess performance in a C-Arm geometry with a FOM of up to 20cm. If scatter estimation is based on simple detruncation algorithms like a constant or a cosine detruncation scatter is estimated inaccurately, resulting in incorrect CT-values as well as streak artifacts in the corrected volume. For the dental CBCT phantom measurement CT-values for soft tissue were corrected from -204HU (no scatter correction) to -87HU (no detruncation), -218HU (constant detruncation), -141HU (cosine detruncation), -91HU (adaptive detruncation), -34HU (prior-based detruncation using a different prior) and -24HU (prior-based detruncation using the identical prior) for a reference value of -26HU measured in slit scan mode. In all cases the prior-based detruncation results in the best scatter correction, followed by the adaptive detruncation, as these algorithms provide a rather accurate model of high-density structures outside the FOM, compared to a simple constant or a cosine detruncation. Our contribution is twofold: first we give a comprehensive comparison of various detruncation methods for the purpose of scatter estimation. We find that the choice of the detruncation method has a significant influence on the quality of MC-based scatter correction. Simple or no detruncation is often insufficient for artifact removal and results in inaccurate CT-values. On the contrary, prior-based detruncation can achieve a high CT-value accuracy and nearly artifact-free volumes from truncated CBCT data when combined with other state-of-the-art artifact corrections. Secondly, we show that prior-based detruncation is effective even with data from a different patient or phantom. The fact that data completion does not require data from the same patient dramatically increases the applicability and usability of this scatter estimation.