diff --git a/README.md b/README.md
index 727f979..f701318 100644
--- a/README.md
+++ b/README.md
@@ -48,8 +48,10 @@ The script will do its best to detect mitigations, including backported non-vani
 This tool does its best to determine whether your system is immune (or has proper mitigations in place) for the collectively named "speculative execution" vulnerabilities. It doesn't attempt to run any kind of exploit, and can't guarantee that your system is secure, but rather helps you verifying whether your system has the known correct mitigations in place.
 However, some mitigations could also exist in your kernel that this script doesn't know (yet) how to detect, or it might falsely detect mitigations that in the end don't work as expected (for example, on backported or modified kernels).
 
-Your system exposure also depends on your CPU. As of now, AMD and ARM processors are marked as immune to some or all of these vulnerabilities (except some specific ARM models). All Intel processors manufactured since circa 1995 are thought to be vulnerable. Whatever processor one uses, one might seek more information from the manufacturer of that processor and/or of the device in which it runs.
+Your system exposure also depends on your CPU. As of now, AMD and ARM processors are marked as immune to some or all of these vulnerabilities (except some specific ARM models). All Intel processors manufactured since circa 1995 are thought to be vulnerable, except some specific/old models, such as some early Atoms. Whatever processor one uses, one might seek more information from the manufacturer of that processor and/or of the device in which it runs.
 
 The nature of the discovered vulnerabilities being quite new, the landscape of vulnerable processors can be expected to change over time, which is why this script makes the assumption that all CPUs are vulnerable, except if the manufacturer explicitly stated otherwise in a verifiable public announcement.
 
+Please also note that for Spectre vulnerabilities, all software can possibly be exploited, this tool only verifies that the kernel (which is the core of the system) you're using has the proper protections in place. Verifying all the other software is out of the scope of this tool. As a general measure, ensure you always have the most up to date stable versions of all the softwares you use, especially for those who are exposed to the world, such as network daemons and browsers.
+
 This tool has been released in the hope that it'll be useful, but don't use it to jump to conclusions about your security.
diff --git a/spectre-meltdown-checker.sh b/spectre-meltdown-checker.sh
index e9761fc..2790f0d 100755
--- a/spectre-meltdown-checker.sh
+++ b/spectre-meltdown-checker.sh
@@ -65,14 +65,19 @@ However, some mitigations could also exist in your kernel that this script doesn
 falsely detect mitigations that in the end don't work as expected (for example, on backported or modified kernels).
 
 Your system exposure also depends on your CPU. As of now, AMD and ARM processors are marked as immune to some or all of these
-vulnerabilities (except some specific ARM models). All Intel processors manufactured since circa 1995 are thought to be vulnerable.
-Whatever processor one uses, one might seek more information from the manufacturer of that processor and/or of the device
-in which it runs.
+vulnerabilities (except some specific ARM models). All Intel processors manufactured since circa 1995 are thought to be vulnerable,
+except some specific/old models, such as some early Atoms. Whatever processor one uses, one might seek more information
+from the manufacturer of that processor and/or of the device in which it runs.
 
 The nature of the discovered vulnerabilities being quite new, the landscape of vulnerable processors can be expected
 to change over time, which is why this script makes the assumption that all CPUs are vulnerable, except if the manufacturer
 explicitly stated otherwise in a verifiable public announcement.
 
+Please also note that for Spectre vulnerabilities, all software can possibly be exploited, this tool only verifies that the
+kernel (which is the core of the system) you're using has the proper protections in place. Verifying all the other software
+is out of the scope of this tool. As a general measure, ensure you always have the most up to date stable versions of all
+the softwares you use, especially for those who are exposed to the world, such as network daemons and browsers.
+
 This tool has been released in the hope that it'll be useful, but don't use it to jump to conclusions about your security.
 
 EOF