Transformer language models (TLMs) are critical for most NLP tasks, but they are difficult to create for low-resource languages because of how much pretraining data they require. In this work, we investigate two techniques for training monolingual TLMs in a low-resource setting: greatly reducing TLM size, and complementing the masked language modeling objective with two linguistically rich supervised tasks (part-of-speech tagging and dependency parsing). Results from 7 diverse languages indicate that our model, MicroBERT, is able to produce marked improvements in downstream task evaluations relative to a typical monolingual TLM pretraining approach. Specifically, we find that monolingual MicroBERT models achieve gains of up to 18% for parser LAS and 11% for NER F1 compared to a multilingual baseline, mBERT, while having less than 1% of its parameter count. We conclude reducing TLM parameter count and using labeled data for pretraining low-resource TLMs can yield large quality benefits and in some cases produce models that outperform multilingual approaches.