diff --git a/.cirrus.yml b/.cirrus.yml
index 9ad96e2cdd..9ae936766a 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -1,6 +1,6 @@
 env:  # Global defaults
   PACKAGE_MANAGER_INSTALL: "apt-get update && apt-get install -y"
-  MAKEJOBS: "-j4"
+  MAKEJOBS: "-j10"
   TEST_RUNNER_PORT_MIN: "14000"  # Must be larger than 12321, which is used for the http cache. See https://cirrus-ci.org/guide/writing-tasks/#http-cache
   CCACHE_SIZE: "200M"
   CCACHE_DIR: "/tmp/ccache_dir"
@@ -38,6 +38,7 @@ main_template: &MAIN_TEMPLATE
     # https://cirrus-ci.org/faq/#are-there-any-limits
     # Each project has 16 CPU in total, assign 2 to each container, so that 8 tasks run in parallel
     cpu: 2
+    greedy: true
     memory: 8G  # Set to 8GB to avoid OOM. https://cirrus-ci.org/guide/linux/#linux-containers
   ccache_cache:
     folder: "/tmp/ccache_dir"
@@ -212,7 +213,6 @@ task:
     memory: 24G
   env:
     << : *CIRRUS_EPHEMERAL_WORKER_TEMPLATE_ENV
-    MAKEJOBS: "-j8"
     FILE_ENV: "./ci/test/00_setup_env_native_tsan.sh"
 
 task:
@@ -223,6 +223,7 @@ task:
   env:
     << : *CIRRUS_EPHEMERAL_WORKER_TEMPLATE_ENV
     FILE_ENV: "./ci/test/00_setup_env_native_msan.sh"
+    MAKEJOBS: "-j4"  # Avoid excessive memory use due to MSan
 
 task:
   name: '[ASan + LSan + UBSan + integer, no depends] [jammy]'
@@ -232,6 +233,7 @@ task:
   env:
     << : *CIRRUS_EPHEMERAL_WORKER_TEMPLATE_ENV
     FILE_ENV: "./ci/test/00_setup_env_native_asan.sh"
+    MAKEJOBS: "-j4"  # Avoid excessive memory use
 
 task:
   name: '[fuzzer,address,undefined,integer, no depends] [focal]'
@@ -243,7 +245,6 @@ task:
     memory: 16G
   env:
     << : *CIRRUS_EPHEMERAL_WORKER_TEMPLATE_ENV
-    MAKEJOBS: "-j8"
     FILE_ENV: "./ci/test/00_setup_env_native_fuzz.sh"
 
 task:
@@ -255,7 +256,6 @@ task:
     memory: 16G  # The default memory is sometimes just a bit too small, so double everything
   env:
     << : *CIRRUS_EPHEMERAL_WORKER_TEMPLATE_ENV
-    MAKEJOBS: "-j8"
     FILE_ENV: "./ci/test/00_setup_env_i686_multiprocess.sh"
 
 task: