We introduce Tied-LoRA, a novel paradigm leveraging weight tying and selective training to enhance the parameter efficiency of Low-rank Adaptation (LoRA). Our exploration encompasses different plausible combinations of parameter training and freezing, coupled with weight tying, aimed at identifying the optimal trade-off between performance and the count of trainable parameters. Across $5$ diverse tasks and two foundational language models with different parameter counts, our experiments provide comprehensive insights into the inherent trade-offs between efficiency and performance. Our findings reveal a specific Tied-LoRA configuration that distinguishes itself by showcasing comparable performance to LoRA across multiple tasks while utilizing only a fraction of the parameters employed by the standard LoRA method, particularly at elevated ranks. This underscores the efficacy of Tied-LoRA in achieving impressive results with significantly reduced model complexity.