diff --git a/doc/manual/source/command-ref/nix-shell.md b/doc/manual/source/command-ref/nix-shell.md
index f2e2e3593..307f1934a 100644
--- a/doc/manual/source/command-ref/nix-shell.md
+++ b/doc/manual/source/command-ref/nix-shell.md
@@ -19,7 +19,7 @@
 
 This man page describes the command `nix-shell`, which is distinct from `nix
 shell`. For documentation on the latter, run `nix shell --help` or see `man
-nix3-shell`.
+nix3-env-shell`.
 
 # Description
 
diff --git a/src/libstore/include/nix/store/globals.hh b/src/libstore/include/nix/store/globals.hh
index 0d6f380a2..8aa82c4a2 100644
--- a/src/libstore/include/nix/store/globals.hh
+++ b/src/libstore/include/nix/store/globals.hh
@@ -199,7 +199,7 @@ public:
           -->
           For instance, in Nixpkgs, if the attribute `enableParallelBuilding` for the `mkDerivation` build helper is set to `true`, it passes the `-j${NIX_BUILD_CORES}` flag to GNU Make.
 
-          If set to `0`, nix will detect the number of CPU cores and pass this number via NIX_BUILD_CORES.
+          If set to `0`, nix will detect the number of CPU cores and pass this number via `NIX_BUILD_CORES`.
 
           > **Note**
           >
diff --git a/src/nix/unix/daemon.cc b/src/nix/unix/daemon.cc
index cb105a385..33ad8757a 100644
--- a/src/nix/unix/daemon.cc
+++ b/src/nix/unix/daemon.cc
@@ -87,7 +87,7 @@ struct AuthorizationSettings : Config
         {"*"},
         "allowed-users",
         R"(
-          A list user names, separated by whitespace.
+          A list of user names, separated by whitespace.
           These users are allowed to connect to the Nix daemon.
 
           You can specify groups by prefixing names with `@`.