diff --git a/debian/changelog b/debian/changelog
index 2ddbfccd7..bbbe8bc99 100644
--- a/debian/changelog
+++ b/debian/changelog
@@ -11,6 +11,8 @@ linux (4.19.16-2) UNRELEASED; urgency=medium
     tools
   * debian/rules.d: Delete now-unused recursive makefiles
   * debian/rules.d/tools/perf/Makefile: Delete redundant arch/profile checks
+  * debian/control: Add !pkg.linux.nokernel to qualification for compiler
+    build-deps
 
  -- Luca Boccassi <bluca@debian.org>  Fri, 18 Jan 2019 19:09:06 +0000
 
diff --git a/debian/config/amd64/defines b/debian/config/amd64/defines
index 1f8a0ad9c..75705b2a8 100644
--- a/debian/config/amd64/defines
+++ b/debian/config/amd64/defines
@@ -16,7 +16,7 @@ install-stem: vmlinuz
 breaks: xserver-xorg-input-vmmouse (<< 1:13.0.99)
 
 [relations]
-gcc-8: gcc-8 (>= 8-20180123-1~) <!stage1 !cross>, gcc-8-x86-64-linux-gnu (>= 8-20180123-1~) <!stage1 cross>
+gcc-8: gcc-8 (>= 8-20180123-1~) <!stage1 !cross !pkg.linux.nokernel>, gcc-8-x86-64-linux-gnu (>= 8-20180123-1~) <!stage1 cross !pkg.linux.nokernel>
 headers%gcc-8: linux-compiler-gcc-8-x86
 
 [amd64_description]
diff --git a/debian/config/defines b/debian/config/defines
index 962e0b7fa..7548a8df6 100644
--- a/debian/config/defines
+++ b/debian/config/defines
@@ -140,7 +140,7 @@ recommends: apparmor
 
 [relations]
 # compilers
-gcc-8: gcc-8 <!stage1 !cross>, gcc-8-@gnu-type-package@ <!stage1 cross>
+gcc-8: gcc-8 <!stage1 !cross !pkg.linux.nokernel>, gcc-8-@gnu-type-package@ <!stage1 cross !pkg.linux.nokernel>
 
 # initramfs-generators
 initramfs-fallback: linux-initramfs-tool
diff --git a/debian/config/hppa/defines b/debian/config/hppa/defines
index 3ba6500e2..263efcc83 100644
--- a/debian/config/hppa/defines
+++ b/debian/config/hppa/defines
@@ -28,5 +28,5 @@ hardware: multiprocessor 64-bit PA-RISC
 hardware-long: HP PA-RISC 64-bit SMP systems with support for more than 4 GB RAM
 
 [relations]
-gcc-8: gcc-8 <!stage1 !cross>, gcc-8-hppa-linux-gnu <!stage1 cross>, binutils-hppa64-linux-gnu <!stage1>, gcc-8-hppa64-linux-gnu <!stage1>
+gcc-8: gcc-8 <!stage1 !cross !pkg.linux.nokernel>, gcc-8-hppa-linux-gnu <!stage1 cross !pkg.linux.nokernel>, binutils-hppa64-linux-gnu <!stage1 !pkg.linux.nokernel>, gcc-8-hppa64-linux-gnu <!stage1 !pkg.linux.nokernel>
 
diff --git a/debian/config/i386/defines b/debian/config/i386/defines
index b737b2030..c093bcc03 100644
--- a/debian/config/i386/defines
+++ b/debian/config/i386/defines
@@ -21,7 +21,7 @@ install-stem: vmlinuz
 breaks: xserver-xorg-input-vmmouse (<< 1:13.0.99)
 
 [relations]
-gcc-8: gcc-8 (>= 8-20180123-1~) <!stage1 !cross>, gcc-8-x86-64-linux-gnu (>= 8-20180123-1~) <!stage1 cross>
+gcc-8: gcc-8 (>= 8-20180123-1~) <!stage1 !cross !pkg.linux.nokernel>, gcc-8-x86-64-linux-gnu (>= 8-20180123-1~) <!stage1 cross !pkg.linux.nokernel>
 headers%gcc-8: linux-compiler-gcc-8-x86
 
 [686_description]