This paper analyzes the design of student assignment mechanisms in school choice, focusing on two competing mechanisms: the Gale-Shapley student optimal stable mechanism and the top trading cycles mechanism. The school choice problem involves assigning students to schools based on priorities and preferences, with the goal of ensuring fair and efficient allocation. Existing school choice plans have significant shortcomings, leading to appeals by unsatisfied parents. The paper evaluates these plans and proposes two alternative mechanisms that may provide practical solutions. The Gale-Shapley student optimal stable mechanism is based on the college admissions problem and is strategy-proof, meaning students cannot benefit by misrepresenting their preferences. It ensures that no student prefers a school over their assigned one, and the school prefers a student over one of its current students. However, it may not always be Pareto efficient, as it can result in outcomes that are dominated by other allocations. The top trading cycles mechanism is another strategy-proof mechanism that is Pareto efficient. It allows students to trade priorities among themselves, starting with those with the highest priorities. This mechanism is a generalization of the random serial dictatorship and can accommodate different priorities at different schools. It is also efficient and ensures that students do not need to manipulate their preferences. Both mechanisms are evaluated in the context of controlled choice, where racial and ethnic balance is maintained. The Gale-Shapley mechanism can be modified to accommodate type-specific quotas, ensuring that certain groups are prioritized. Similarly, the top trading cycles mechanism can be adapted to include type-specific quotas, ensuring that students are assigned seats based on their type. The paper concludes that both mechanisms are effective in addressing school choice issues, with the choice between them depending on the priorities of policy-makers. The Gale-Shapley mechanism is preferred when complete elimination of justified envy is prioritized, while the top trading cycles mechanism is preferred when efficiency is the main concern. Both mechanisms are strategy-proof and can be adapted to accommodate controlled choice constraints, ensuring fair and efficient school assignments.This paper analyzes the design of student assignment mechanisms in school choice, focusing on two competing mechanisms: the Gale-Shapley student optimal stable mechanism and the top trading cycles mechanism. The school choice problem involves assigning students to schools based on priorities and preferences, with the goal of ensuring fair and efficient allocation. Existing school choice plans have significant shortcomings, leading to appeals by unsatisfied parents. The paper evaluates these plans and proposes two alternative mechanisms that may provide practical solutions. The Gale-Shapley student optimal stable mechanism is based on the college admissions problem and is strategy-proof, meaning students cannot benefit by misrepresenting their preferences. It ensures that no student prefers a school over their assigned one, and the school prefers a student over one of its current students. However, it may not always be Pareto efficient, as it can result in outcomes that are dominated by other allocations. The top trading cycles mechanism is another strategy-proof mechanism that is Pareto efficient. It allows students to trade priorities among themselves, starting with those with the highest priorities. This mechanism is a generalization of the random serial dictatorship and can accommodate different priorities at different schools. It is also efficient and ensures that students do not need to manipulate their preferences. Both mechanisms are evaluated in the context of controlled choice, where racial and ethnic balance is maintained. The Gale-Shapley mechanism can be modified to accommodate type-specific quotas, ensuring that certain groups are prioritized. Similarly, the top trading cycles mechanism can be adapted to include type-specific quotas, ensuring that students are assigned seats based on their type. The paper concludes that both mechanisms are effective in addressing school choice issues, with the choice between them depending on the priorities of policy-makers. The Gale-Shapley mechanism is preferred when complete elimination of justified envy is prioritized, while the top trading cycles mechanism is preferred when efficiency is the main concern. Both mechanisms are strategy-proof and can be adapted to accommodate controlled choice constraints, ensuring fair and efficient school assignments.