Deploying Machine learning (ML) on the milliwatt-scale edge devices (tinyML) is gaining popularity due to recent breakthroughs in ML and IoT. However, the capabilities of tinyML are restricted by strict power and compute constraints. The majority of the contemporary research in tinyML focuses on model compression techniques such as model pruning and quantization to fit ML models on low-end devices. Nevertheless, the improvements in energy consumption and inference time obtained by existing techniques are limited because aggressive compression quickly shrinks model capacity and accuracy. Another approach to improve inference time and/or reduce power while preserving its model capacity is through early-exit networks. These networks place intermediate classifiers along a baseline neural network that facilitate early exit from neural network computation if an intermediate classifier exhibits sufficient confidence in its prediction. Previous work on early-exit networks have focused on large networks, beyond what would typically be used for tinyML applications. In this paper, we discuss the challenges of adding early-exits to state-of-the-art tiny-CNNs and devise an early-exit architecture, T-RECX, that addresses these challenges. In addition, we develop a method to alleviate the effect of network overthinking at the final exit by leveraging the high-level representations learned by the early-exit. We evaluate T-RECX on three CNNs from the MLPerf tiny benchmark suite for image classification, keyword spotting and visual wake word detection tasks. Our results demonstrate that T-RECX improves the accuracy of baseline network and significantly reduces the average inference time of tiny-CNNs. T-RECX achieves 32.58% average reduction in FLOPS in exchange for 1% accuracy across all evaluated models. Also, our techniques increase the accuracy of baseline network in two out of three models we evaluate