diff --git a/INSTALL b/INSTALL
index e5143c6b7..e9d38f931 100644
--- a/INSTALL
+++ b/INSTALL
@@ -285,7 +285,10 @@ systems, by passing "USE_SLZ=" to the "make" command.
 
 Please note that SLZ will benefit from some CPU-specific instructions like the
 availability of the CRC32 extension on some ARM processors. Thus it can further
-improve its performance to build with "CPU=native" on the target system.
+improve its performance to build with "CPU=native" on the target system, or
+"CPU=armv81" (modern systems such as Graviton2 or A55/A75 and beyond),
+"CPU=a72" (e.g. for RPi4, or AWS Graviton), "CPU=a53" (e.g. for RPi3), or
+"CPU=armv8-auto" (automatic detection with minor runtime penalty).
 
 A second option involves the widely known zlib library, which is very likely
 installed on your system. In order to use zlib, simply pass "USE_ZLIB=1" to the
@@ -421,6 +424,11 @@ one of the following choices to the CPU variable :
   - ultrasparc : Sun UltraSparc I/II/III/IV processor
   - power8 : IBM POWER8 processor
   - power9 : IBM POWER9 processor
+  - armv81 : modern ARM cores (Cortex A55/A75/A76/A78/X1, Neoverse, Graviton2)
+  - a72    : ARM Cortex-A72 or A73 (e.g. RPi4, Odroid N2, AWS Graviton)
+  - a53    : ARM Cortex-A53 or any of its successors in 64-bit mode (e.g. RPi3)
+  - armv8-auto : support both older and newer armv8 cores with a minor penalty,
+                 thanks to gcc 10's outline atomics (default with gcc 10.2).
   - native : use the build machine's specific processor optimizations. Use with
     extreme care, and never in virtualized environments (known to break).
   - generic : any other processor or no CPU-specific optimization. (default)
diff --git a/Makefile b/Makefile
index 74fca3529..6571dc6fc 100644
--- a/Makefile
+++ b/Makefile
@@ -162,7 +162,8 @@ TARGET =
 #### TARGET CPU
 # Use CPU=<cpu_name> to optimize for a particular CPU, among the following
 # list :
-#    generic, native, i586, i686, ultrasparc, power8, power9, custom
+#    generic, native, i586, i686, ultrasparc, power8, power9, custom,
+#    a53, a72, armv81, armv8-auto
 CPU = generic
 
 #### Architecture, used when not building for native architecture
@@ -274,6 +275,10 @@ CPU_CFLAGS.i686       = -O2 -march=i686
 CPU_CFLAGS.ultrasparc = -O6 -mcpu=v9 -mtune=ultrasparc
 CPU_CFLAGS.power8     = -O2 -mcpu=power8 -mtune=power8
 CPU_CFLAGS.power9     = -O2 -mcpu=power9 -mtune=power9
+CPU_CFLAGS.a53        = -O2 -mcpu=cortex-a53
+CPU_CFLAGS.a72        = -O2 -mcpu=cortex-a72
+CPU_CFLAGS.armv81     = -O2 -march=armv8.1-a
+CPU_CFLAGS.armv8-auto = -O2 -march=armv8-a+crc -moutline-atomics
 CPU_CFLAGS            = $(CPU_CFLAGS.$(CPU))
 
 #### ARCH dependent flags, may be overridden by CPU flags