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While technical debt grows in absolute numbers as software systems evolve over time, the density of technical debt (technical debt divided by lines of code) is reduced in some cases. This can be explained by either the application of refactorings or the development of new artifacts with limited Technical Debt. In this paper we explore the second explanation, by investigating the relation between the amount of Technical Debt in new code and the evolution of Technical Debt in the system. To this end, we compare the Technical Debt Density of new code with existing code, and we investigate which of the three major types of code changes (additions, deletions and modifications) is primarily responsible for changes in the evolution of Technical Debt density. Furthermore, we study whether there is a relation between code quality practices and the 'cleanness' of new code. To obtain the required data, we have performed a large-scale case study on twenty-seven open-source software projects by the Apache Software Foundation, analyzing 66,661 classes and 56,890 commits. The results suggest that writing "clean" (or at least "cleaner") new code can be an efficient strategy for reducing Technical Debt Density, and thus preventing software decay over time. The findings also suggest that projects adopting an explicit policy for quality improvement, e.g. through discussions on code quality in board meetings, are associated with a higher frequency of cleaner new code commits. Therefore, we champion the establishment of processes that monitor the density of Technical Debt of new code to control the accumulation of Technical Debt in a software system.