diff --git a/.cirrus.yml b/.cirrus.yml
index c82983526d5fd..6a3b4b2ebc78f 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -63,27 +63,8 @@ task:
     - env: {BUILD: distcheck, WITH_VALGRIND: no, CTIMETEST: no, BENCH: no}
     - env: {CPPFLAGS: -DDETERMINISTIC}
     - env: {CFLAGS: -O0, CTIMETEST: no}
-    - env:
-        CFLAGS:  "-fsanitize=undefined -fno-omit-frame-pointer"
-        LDFLAGS: "-fsanitize=undefined -fno-omit-frame-pointer"
-        UBSAN_OPTIONS: "print_stacktrace=1:halt_on_error=1"
-        ASM: x86_64
-        ECDH: yes
-        RECOVERY: yes
-        EXPERIMENTAL: yes
-        SCHNORRSIG: yes
-        CTIMETEST: no
     - env: { ECMULTGENPRECISION: 2 }
     - env: { ECMULTGENPRECISION: 8 }
-    - env:
-        RUN_VALGRIND: yes
-        ASM: x86_64
-        ECDH: yes
-        RECOVERY: yes
-        EXPERIMENTAL: yes
-        SCHNORRSIG: yes
-        EXTRAFLAGS: "--disable-openssl-tests"
-        BUILD:
   matrix:
     - env:
         CC: gcc
@@ -262,3 +243,48 @@ task:
   test_script:
     - ./ci/cirrus.sh
   << : *CAT_LOGS
+
+# Sanitizers
+task:
+  container:
+    dockerfile: ci/linux-debian.Dockerfile
+    cpu: 1
+    memory: 1G
+  env:
+    ECDH: yes
+    RECOVERY: yes
+    EXPERIMENTAL: yes
+    SCHNORRSIG: yes
+    CTIMETEST: no
+    EXTRAFLAGS: "--disable-openssl-tests"
+  matrix:
+    - name: "Valgrind (memcheck)"
+      env:
+        RUN_VALGRIND: yes
+    - name: "UBSan, ASan, LSan"
+      env:
+        CFLAGS: "-fsanitize=undefined,address"
+        CFLAGS_FOR_BUILD: "-fsanitize=undefined,address"
+        UBSAN_OPTIONS: "print_stacktrace=1:halt_on_error=1"
+        ASAN_OPTIONS: "strict_string_checks=1:detect_stack_use_after_return=1:detect_leaks=1"
+        LSAN_OPTIONS: "use_unaligned=1"
+  # Try to cover many configurations with just a tiny matrix.
+  matrix:
+    - env:
+        ASM: auto
+        STATICPRECOMPUTATION: yes
+    - env:
+        ASM: no
+        STATICPRECOMPUTATION: no
+        ECMULTGENPRECISION: 2
+  matrix:
+    - env:
+        CC: clang
+    - env:
+        HOST: i686-linux-gnu
+        CC: i686-linux-gnu-gcc
+  << : *MERGE_BASE
+  test_script:
+    - ./ci/cirrus.sh
+  << : *CAT_LOGS
+
diff --git a/ci/linux-debian.Dockerfile b/ci/linux-debian.Dockerfile
index 6559c58021542..e06c816686534 100644
--- a/ci/linux-debian.Dockerfile
+++ b/ci/linux-debian.Dockerfile
@@ -7,11 +7,12 @@ RUN dpkg --add-architecture arm64
 RUN apt-get update
 
 # dkpg-dev: to make pkg-config work in cross-builds
+# llvm: for llvm-symbolizer, which is used by clang's UBSan for symbolized stack traces
 RUN apt-get install --no-install-recommends --no-upgrade -y \
         git ca-certificates \
         make automake libtool pkg-config dpkg-dev valgrind qemu-user \
-        gcc clang libc6-dbg \
-        gcc-i686-linux-gnu libc6-dev-i386-cross libc6-dbg:i386 \
+        gcc clang llvm libc6-dbg \
+        gcc-i686-linux-gnu libc6-dev-i386-cross libc6-dbg:i386 libubsan1:i386 libasan5:i386 \
         gcc-s390x-linux-gnu libc6-dev-s390x-cross libc6-dbg:s390x \
         gcc-arm-linux-gnueabihf libc6-dev-armhf-cross libc6-dbg:armhf \
         gcc-aarch64-linux-gnu libc6-dev-arm64-cross libc6-dbg:arm64 \