diff --git a/Cargo.toml b/Cargo.toml
index 147d8ce26..31faa5f0d 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -23,6 +23,7 @@ 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"]
 recovery = ["secp256k1-sys/recovery"]
 lowmemory = ["secp256k1-sys/lowmemory"]
@@ -37,10 +38,12 @@ global-context-less-secure = []
 
 [dependencies]
 secp256k1-sys = { version = "0.4.2", default-features = false, path = "./secp256k1-sys" }
+serde = { version = "1.0", default-features = false, optional = true }
 
+# 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 }
 
 [dev-dependencies]
 rand = "0.6"
diff --git a/contrib/test.sh b/contrib/test.sh
index c79d3f8ea..5ac08d045 100755
--- a/contrib/test.sh
+++ b/contrib/test.sh
@@ -1,7 +1,10 @@
 #!/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"
+# These features are typically enabled along with the 'std' feature, so we test
+# them together with 'std'.
+STD_FEATURES="rand-std bitcoin-hashes-std"
 
 # Use toolchain if explicitly specified
 if [ -n "$TOOLCHAIN" ]
@@ -32,11 +35,15 @@ if [ "$DO_FEATURE_MATRIX" = true ]; then
         cargo build --all --no-default-features --features="$feature"
         cargo test --all --no-default-features --features="$feature"
     done
-
+    # Features tested with 'std' feature enabled.
+    for feature in ${FEATURES}
+    do
+        cargo build --all --no-default-features --features="std,$feature"
+        cargo test --all --no-default-features --features="std,$feature"
+    done
     # Other combos 
     RUSTFLAGS='--cfg=fuzzing' RUSTDOCFLAGS=$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"
 
     if [ "$DO_BENCH" = true ]; then  # proxy for us having a nightly compiler