diff --git a/base/mpfr.jl b/base/mpfr.jl
index 8f12968c4a701..289f43a0bebd5 100644
--- a/base/mpfr.jl
+++ b/base/mpfr.jl
@@ -66,14 +66,16 @@ type BigFloat <: AbstractFloat
     sign::Cint
     exp::Clong
     d::Ptr{Limb}
+
     function BigFloat()
-        N = precision(BigFloat)
+        prec = precision(BigFloat)
         z = new(zero(Clong), zero(Cint), zero(Clong), C_NULL)
-        ccall((:mpfr_init2,:libmpfr), Void, (Ptr{BigFloat}, Clong), &z, N)
+        ccall((:mpfr_init2,:libmpfr), Void, (Ptr{BigFloat}, Clong), &z, prec)
         finalizer(z, cglobal((:mpfr_clear, :libmpfr)))
         return z
     end
-    # Not recommended for general use
+
+    # Not recommended for general use:
     function BigFloat(prec::Clong, sign::Cint, exp::Clong, d::Ptr{Void})
         new(prec, sign, exp, d)
     end
@@ -118,6 +120,46 @@ end
 convert(::Type{Rational}, x::BigFloat) = convert(Rational{BigInt}, x)
 convert(::Type{AbstractFloat}, x::BigInt) = BigFloat(x)
 
+# generic constructor with arbitrary precision:
+"""
+    BigFloat(x, prec::Int)
+
+Create a representation of `x` as a `BigFloat` with precision `prec`.
+"""
+function BigFloat(x, prec::Int)
+    setprecision(BigFloat, prec) do
+        BigFloat(x)
+    end
+end
+
+"""
+    BigFloat(x, prec::Int, rounding::RoundingMode)
+
+Create a representation of `x` as a `BigFloat` with precision `prec` and rounding mode `rounding`.
+"""
+function BigFloat(x, prec::Int, rounding::RoundingMode)
+    setrounding(BigFloat, rounding) do
+        BigFloat(x, prec)
+    end
+end
+
+"""
+    BigFloat(x, rounding::RoundingMode)
+
+Create a representation of `x` as a `BigFloat` with the current global precision and rounding mode `rounding`.
+"""
+function BigFloat(x::Union{Integer, AbstractFloat, String}, rounding::RoundingMode)
+    BigFloat(x, precision(BigFloat), rounding)
+end
+
+"""
+    BigFloat(x::String)
+
+Create a representation of the string `x` as a `BigFloat`.
+"""
+BigFloat(x::String) = parse(BigFloat, x)
+
+
 ## BigFloat -> Integer
 function unsafe_cast(::Type{Int64}, x::BigFloat, ri::Cint)
     ccall((:__gmpfr_mpfr_get_sj,:libmpfr), Cintmax_t,
diff --git a/doc/src/stdlib/numbers.md b/doc/src/stdlib/numbers.md
index 908bf2b236701..715a8319f9b18 100644
--- a/doc/src/stdlib/numbers.md
+++ b/doc/src/stdlib/numbers.md
@@ -102,11 +102,20 @@ The `BigFloat` type implements arbitrary-precision floating-point arithmetic usi
 
 ```@docs
 Base.precision
+Base.MPFR.precision(::Type{BigFloat})
 Base.MPFR.setprecision
 ```
 
+### Additional constructors for `BigFloat`
+```@docs
+Base.MPFR.BigFloat(x, prec::Int)
+BigFloat(x::Union{Integer, AbstractFloat, String}, rounding::RoundingMode)
+Base.MPFR.BigFloat(x, prec::Int, rounding::RoundingMode)
+Base.MPFR.BigFloat(x::String)
+```
 ## Random Numbers
 
+
 Random number generation in Julia uses the [Mersenne Twister library](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/#dSFMT)
 via `MersenneTwister` objects. Julia has a global RNG, which is used by default. Other RNG types
 can be plugged in by inheriting the `AbstractRNG` type; they can then be used to have multiple
diff --git a/test/mpfr.jl b/test/mpfr.jl
index cbef129d71a6e..2660e151cf218 100644
--- a/test/mpfr.jl
+++ b/test/mpfr.jl
@@ -873,3 +873,26 @@ let b = IOBuffer()
 end
 
 @test isnan(sqrt(BigFloat(NaN)))
+
+# PR 17217 -- BigFloat constructors with given precision and rounding mode
+
+# test constructors and `big` with additional precision and rounding mode:
+
+for prec in (10, 100, 1000)
+    for val in ("3.1", pi, "-1.3", 3.1)
+        let
+            a = BigFloat(val)
+            b = BigFloat(val, prec)
+            c = BigFloat(val, RoundUp)
+            d = BigFloat(val, prec, RoundDown)
+            e = BigFloat(val, prec, RoundUp)
+
+            @test precision(a) == precision(BigFloat)
+            @test precision(b) == prec
+            @test precision(c) == precision(BigFloat)
+            @test precision(d) == prec
+            @test precision(e) == prec
+            (val != 3.1) && @test e > d     # rounding has no effect when constructing from Float64
+        end
+    end
+end