diff --git a/pkg/cmd/teamcity-trigger/main.go b/pkg/cmd/teamcity-trigger/main.go
index 6b1ec3d0f411..40510014ad9a 100644
--- a/pkg/cmd/teamcity-trigger/main.go
+++ b/pkg/cmd/teamcity-trigger/main.go
@@ -54,21 +54,44 @@ func main() {
 	})
 }
 
-func runTC(queueBuild func(string, map[string]string)) {
-	importPaths := gotool.ImportPaths([]string{"github.com/cockroachdb/cockroach/pkg/..."})
+const baseImportPath = "github.com/cockroachdb/cockroach/pkg/"
+
+var importPaths = gotool.ImportPaths([]string{baseImportPath + "..."})
 
+func runTC(queueBuild func(string, map[string]string)) {
 	// Queue stress builds. One per configuration per package.
-	for _, opts := range []map[string]string{
-		{}, // uninstrumented
-		// The race detector is CPU intensive, so we want to run less processes in
-		// parallel. (Stress, by default, will run one process per CPU.)
+	for _, importPath := range importPaths {
+		// The stress program by default runs as many instances in parallel as there
+		// are CPUs. Each instance itself can run tests in parallel. The amount of
+		// parallelism needs to be reduced, or we can run into OOM issues,
+		// especially for race builds and/or logic tests (see
+		// https://github.com/cockroachdb/cockroach/pull/10966).
 		//
-		// TODO(benesch): avoid assuming that TeamCity agents have eight CPUs.
-		{"env.GOFLAGS": "-race", "env.STRESSFLAGS": "-p 4"},
-	} {
-		for _, importPath := range importPaths {
-			opts["env.PKG"] = importPath
-			queueBuild("Cockroach_Nightlies_Stress", opts)
+		// We limit both the stress program parallelism and the go test parallelism
+		// to 4 for non-race builds and 2 for race builds. For logic tests, we
+		// halve these values.
+		parallelism := 4
+
+		// Stress logic tests with reduced parallelism (to avoid overloading the
+		// machine, see https://github.com/cockroachdb/cockroach/pull/10966).
+		if importPath == baseImportPath+"sql/logictest" {
+			parallelism /= 2
 		}
+
+		opts := map[string]string{
+			"env.PKG": importPath,
+		}
+
+		// Run non-race build.
+		opts["env.GOFLAGS"] = fmt.Sprintf("-parallel=%d", parallelism)
+		opts["env.STRESSFLAGS"] = fmt.Sprintf("-p %d", parallelism)
+		queueBuild("Cockroach_Nightlies_Stress", opts)
+
+		// Run race build. Reduce the parallelism to avoid overloading the machine.
+		parallelism /= 2
+		opts["env.GOFLAGS"] = fmt.Sprintf("-race -parallel=%d", parallelism)
+		opts["env.STRESSFLAGS"] = fmt.Sprintf("-p %d", parallelism)
+
+		queueBuild("Cockroach_Nightlies_Stress", opts)
 	}
 }
diff --git a/pkg/cmd/teamcity-trigger/main_test.go b/pkg/cmd/teamcity-trigger/main_test.go
index e69c8c043b55..06b1fe85f43c 100644
--- a/pkg/cmd/teamcity-trigger/main_test.go
+++ b/pkg/cmd/teamcity-trigger/main_test.go
@@ -15,6 +15,8 @@
 package main
 
 import (
+	"fmt"
+	"sort"
 	"strings"
 	"testing"
 )
@@ -35,3 +37,43 @@ func TestRunTC(t *testing.T) {
 		t.Fatal("no builds were created")
 	}
 }
+
+func Example_runTC() {
+	// Shows sample output for two packages, one of which runs with reduced
+	// parallelism.
+	runTC(func(buildID string, opts map[string]string) {
+		pkg := opts["env.PKG"]
+		if !strings.HasSuffix(pkg, "pkg/sql/logictest") && !strings.HasSuffix(pkg, "pkg/storage") {
+			return
+		}
+		var keys []string
+		for k := range opts {
+			if k != "env.PKG" {
+				keys = append(keys, k)
+			}
+		}
+		sort.Strings(keys)
+		fmt.Println(pkg)
+		for _, k := range keys {
+			fmt.Printf("  %-16s %s\n", k+":", opts[k])
+		}
+		fmt.Println()
+	})
+
+	// Output:
+	// github.com/cockroachdb/cockroach/pkg/sql/logictest
+	//   env.GOFLAGS:     -parallel=2
+	//   env.STRESSFLAGS: -p 2
+	//
+	// github.com/cockroachdb/cockroach/pkg/sql/logictest
+	//   env.GOFLAGS:     -race -parallel=1
+	//   env.STRESSFLAGS: -p 1
+	//
+	// github.com/cockroachdb/cockroach/pkg/storage
+	//   env.GOFLAGS:     -parallel=4
+	//   env.STRESSFLAGS: -p 4
+	//
+	// github.com/cockroachdb/cockroach/pkg/storage
+	//   env.GOFLAGS:     -race -parallel=2
+	//   env.STRESSFLAGS: -p 2
+}
diff --git a/pkg/sql/logictest/logic.go b/pkg/sql/logictest/logic.go
index 0001c2716a19..fcf28b5c5d51 100644
--- a/pkg/sql/logictest/logic.go
+++ b/pkg/sql/logictest/logic.go
@@ -2094,10 +2094,9 @@ var logicTestsConfigFilter = envutil.EnvOrDefaultString("COCKROACH_LOGIC_TESTS_C
 // RunLogicTest is the main entry point for the logic test. The globs parameter
 // specifies the default sets of files to run.
 func RunLogicTest(t *testing.T, globs ...string) {
-	if testutils.NightlyStress() {
-		// See https://github.com/cockroachdb/cockroach/pull/10966.
-		t.Skip()
-	}
+	// Note: there is special code in teamcity-trigger/main.go to run this package
+	// with less concurrency in the nightly stress runs. If you see problems
+	// please make adjustments there.
 
 	if skipLogicTests {
 		t.Skip("COCKROACH_LOGIC_TESTS_SKIP")