diff --git a/Cargo.toml b/Cargo.toml
index 147d8ce26..4ceaad25d 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -23,7 +23,9 @@ default = ["std"]
 std = ["secp256k1-sys/std"]
 # allow use of Secp256k1::new and related API that requires an allocator
 alloc = []
+bitcoin-hashes-std = ["bitcoin_hashes/std"]
 rand-std = ["rand/std"]
+serde-std = ["serde/std"]
 recovery = ["secp256k1-sys/recovery"]
 lowmemory = ["secp256k1-sys/lowmemory"]
 global-context = ["std"]
@@ -38,6 +40,8 @@ global-context-less-secure = []
 [dependencies]
 secp256k1-sys = { version = "0.4.2", default-features = false, path = "./secp256k1-sys" }
 
+# You likely only want to enable these if you explicitly do not want to use "std", otherwise enable
+# the respective -std feature e.g., bitcoin-hashes-std
 bitcoin_hashes = { version = "0.10", default-features = false, optional = true }
 rand = { version = "0.6", default-features = false, optional = true }
 serde = { version = "1.0", default-features = false, optional = true }
diff --git a/contrib/test.sh b/contrib/test.sh
index c79d3f8ea..a74c6babd 100755
--- a/contrib/test.sh
+++ b/contrib/test.sh
@@ -1,7 +1,7 @@
 #!/bin/sh -ex
 
 # TODO: Add "alloc" once we bump MSRV to past 1.29
-FEATURES="bitcoin_hashes global-context lowmemory rand rand-std recovery serde std"
+FEATURES="bitcoin_hashes global-context lowmemory rand recovery serde std"
 
 # Use toolchain if explicitly specified
 if [ -n "$TOOLCHAIN" ]
@@ -36,8 +36,11 @@ if [ "$DO_FEATURE_MATRIX" = true ]; then
     # Other combos 
     RUSTFLAGS='--cfg=fuzzing' RUSTDOCFLAGS=$RUSTFLAGS cargo test --all
     RUSTFLAGS='--cfg=fuzzing' RUSTDOCFLAGS=$RUSTFLAGS cargo test --all --features="$FEATURES"
-    cargo test --all --features="rand rand-std"
     cargo test --all --features="rand serde"
+    # Test features that will likely only be enabled along with `std`.
+    cargo test --all --features="rand-std"
+    cargo test --all --features="bitcoin-hashes-std"
+    cargo test --all --features="serde-std"
 
     if [ "$DO_BENCH" = true ]; then  # proxy for us having a nightly compiler
         cargo test --all --all-features