Kammala jumla mai zuwa: Bronstein ya ɗauki kyaututtukan farko da yawa a gasa, daga cikin sanannun kasancewar Gasar Chess ta Soviet ta 1948 (tare da Alexander Kotov) da 1949 (tare da Smyslov). Ya kuma daidaita a matsayi na biyu a gasar zakarun Soviet na 1957 da 1964-65. Ya yi daidai da Mark Taimanov a gasar zakarun duniya a shekarar 1952 a Liverpool. Bronstein kuma ya lashe gasar zakarun Moscow sau shida, kuma ya wakilci USSR a gasar Olympics ta 1952,
1954, 1956 da 1958, ya lashe kyaututtukan hukumar a kowannensu, kuma ya rasa wasa ɗaya daga cikin wasanninsa 49 a waɗannan abubuwan. A hanya ya lashe lambobin zinare na Olympics guda hudu. A wasan wasan na 1954 da Amurka (wanda aka gudanar a New York), Bronstein ya zira kwallaye kusan ba a taɓa jin irinsa ba a wannan matakin wasan, ya ci dukkan wasanninsa huɗu a tebur na biyu.