diff --git a/Cargo.toml b/Cargo.toml
index 70f266ee50..e1c8a5089a 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -38,6 +38,10 @@ spirv-builder = { path = "./crates/spirv-builder", version = "=0.9.0", default-f
 rustc_codegen_spirv = { path = "./crates/rustc_codegen_spirv", version = "=0.9.0", default-features = false }
 rustc_codegen_spirv-types = { path = "./crates/rustc_codegen_spirv-types", version = "=0.9.0" }
 
+# External dependencies that need to be mentioned more than once.
+num-traits = { version = "0.2.15", default-features = false }
+glam = { version = ">=0.22, <=0.24", default-features = false }
+
 # Enable incremental by default in release mode.
 [profile.release]
 incremental = true
diff --git a/crates/rustc_codegen_spirv/Cargo.toml b/crates/rustc_codegen_spirv/Cargo.toml
index 4b94d02edf..f68c855a47 100644
--- a/crates/rustc_codegen_spirv/Cargo.toml
+++ b/crates/rustc_codegen_spirv/Cargo.toml
@@ -42,7 +42,7 @@ syn = { version = "1", features = ["extra-traits", "full"] }
 # in order to avoid multiple separate instances of `rustc_codegen_spirv`.
 hashbrown = "0.11"
 libc = { version = "0.2", features = ["align", "extra_traits"] }
-num-traits = { version = "0.2", features = ["libm"] }
+num-traits = { workspace = true, default-features = true }
 once_cell = "1"
 regex = { version = "1", features = ["perf"] }
 
diff --git a/crates/spirv-std/Cargo.toml b/crates/spirv-std/Cargo.toml
index 2efdff6223..2ce5b6d0fa 100644
--- a/crates/spirv-std/Cargo.toml
+++ b/crates/spirv-std/Cargo.toml
@@ -11,8 +11,14 @@ repository.workspace = true
 spirv-std-types.workspace = true
 spirv-std-macros.workspace = true
 bitflags = "1.2.1"
-num-traits = { version = "0.2.15", default-features = false, features = ["libm"] }
-glam = { version = ">=0.22, <=0.24", default-features = false, features = ["libm"] }
+
+[target.'cfg(target_arch = "spirv")'.dependencies]
+num-traits = { workspace = true, features = ["libm"] }
+glam = { workspace = true, features = ["libm"] }
+
+[target.'cfg(not(target_arch = "spirv"))'.dependencies]
+num-traits = { workspace = true, default-features = true }
+glam = { workspace = true, default-features = true }
 
 [features]
 default = []